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lib_XC.F
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c The codes in this file were taken from density functional
C repository
c ftp://ftp.dl.ac.uk/qcg/dft_library/index.html
c $Revision: 1.10 $, $Date: 2006/02/01 13:48:18
c The routines are listed below, the rks counterpart are also
C available
c uks_x_lda
c uks_x_b88
c uks_x_pbe
c uks_x_pw91
c uks_c_vwn5
c uks_c_p86
c uks_c_lyp
c uks_c_pw91
c uks_c_pbe
c uks_xc_b97
c uks_xc_hcth407
real*8 function piecewise(o,a,b)
c
c Fix for a Maple problem. The Maple Fortran generator is not
c able to transform its piecewise command to Fortran. Therefore
c this function was written to take care of this.
c
implicit none
logical o
real*8 a, b
if (o) then
piecewise = a
else
piecewise = b
endif
return
end
subroutine uks_x_lda
& (ideriv,npt,rhoa1,rhob1,sigmaaa1,sigmabb1,sigmaab1,
& zk,vrhoa,vrhob,vsigmaaa,vsigmabb,vsigmaab,
& v2rhoa2,v2rhob2,v2rhoab,
& v2rhoasigmaaa,v2rhoasigmaab,v2rhoasigmabb,
& v2rhobsigmabb,v2rhobsigmaab,v2rhobsigmaaa,
& v2sigmaaa2,v2sigmaaaab,v2sigmaaabb,
& v2sigmaab2,v2sigmaabbb,v2sigmabb2)
c
c P.A.M. Dirac
c Proceedings of the Cambridge Philosophical Society, 26 (1930) 376
c
c
c CITATION:
c
c Functionals were obtained from the Density Functional Repository
c as developed and distributed by the Quantum Chemistry Group,
c CCLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD
c United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or
c Paul Sherwood for further information.
c
c COPYRIGHT:
c
c Users may incorporate the source code into software packages and
c redistribute the source code provided the source code is not
c changed in anyway and is properly cited in any documentation or
c publication related to its use.
c
c ACKNOWLEDGEMENT:
c
c The source code was generated using Maple 8 through a modified
c version of the dfauto script published in:
c
c R. Strange, F.R. Manby, P.J. Knowles
c Automatic code generation in density functional theory
c Comp. Phys. Comm. 136 (2001) 310-318.
c
implicit real*8 (a-h,o-z)
integer ideriv,npt
real*8 rhoa1(npt),rhob1(npt)
real*8 sigmaaa1(npt),sigmabb1(npt),sigmaab1(npt)
real*8 zk(npt),vrhoa(npt),vrhob(npt)
real*8 vsigmaaa(npt),vsigmabb(npt),vsigmaab(npt)
real*8 v2rhoa2(npt),v2rhob2(npt),v2rhoab(npt)
real*8 v2rhoasigmaaa(npt),v2rhoasigmaab(npt)
real*8 v2rhoasigmabb(npt),v2rhobsigmabb(npt)
real*8 v2rhobsigmaab(npt),v2rhobsigmaaa(npt)
real*8 v2sigmaaa2(npt),v2sigmaaaab(npt),v2sigmaaabb(npt)
real*8 v2sigmaab2(npt),v2sigmaabbb(npt),v2sigmabb2(npt)
parameter(tol=1.0d-20)
if (ideriv.eq.0) then
do i=1,npt
rhoa = dmax1(0.D0,rhoa1(i))
rhob = dmax1(0.D0,rhob1(i))
rho = rhoa+rhob
if(rho.gt.tol) then
if(rhoa.lt.tol) then
rho = rhob
t1 = rhob**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhob
elseif(rhob.lt.tol) then
rho = rhoa
t1 = rhoa**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhoa
else ! (.not.(rhoa.lt.tol).and..not.(rhob.lt.tol))
t1 = rhoa**(1.D0/3.D0)
t4 = rhob**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhoa-0.9305257363491D0*t4*rhob
endif ! rhoa,rhob
else ! rho
zk(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.1) then
do i=1,npt
rhoa = dmax1(0.D0,rhoa1(i))
rhob = dmax1(0.D0,rhob1(i))
rho = rhoa+rhob
if(rho.gt.tol) then
if(rhoa.lt.tol) then
rho = rhob
t1 = rhob**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhob
vrhoa(i) = 0.D0
vrhob(i) = -0.12407009817988D1*t1
elseif(rhob.lt.tol) then
rho = rhoa
t1 = rhoa**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhoa
vrhoa(i) = -0.12407009817988D1*t1
vrhob(i) = 0.D0
else ! (.not.(rhoa.lt.tol).and..not.(rhob.lt.tol))
t1 = rhoa**(1.D0/3.D0)
t4 = rhob**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhoa-0.9305257363491D0*t4*rhob
vrhoa(i) = -0.12407009817988D1*t1
vrhob(i) = -0.12407009817988D1*t4
endif ! rhoa,rhob
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
vrhob(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.2) then
do i=1,npt
rhoa = dmax1(0.D0,rhoa1(i))
rhob = dmax1(0.D0,rhob1(i))
rho = rhoa+rhob
if(rho.gt.tol) then
if(rhoa.lt.tol) then
rho = rhob
t1 = rhob**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhob
vrhoa(i) = 0.D0
vrhob(i) = -0.12407009817988D1*t1
v2rhoa2(i) = 0.D0
v2rhoab(i) = 0.D0
t5 = t1**2
v2rhob2(i) = -0.4135669939329333D0/t5
elseif(rhob.lt.tol) then
rho = rhoa
t1 = rhoa**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhoa
vrhoa(i) = -0.12407009817988D1*t1
vrhob(i) = 0.D0
t5 = t1**2
v2rhoa2(i) = -0.4135669939329333D0/t5
v2rhob2(i) = 0.D0
v2rhoab(i) = 0.D0
else ! (.not.(rhoa.lt.tol).and..not.(rhob.lt.tol))
t1 = rhoa**(1.D0/3.D0)
t4 = rhob**(1.D0/3.D0)
zk(i) = -0.9305257363491D0*t1*rhoa-0.9305257363491D0*t4*rhob
vrhoa(i) = -0.12407009817988D1*t1
vrhob(i) = -0.12407009817988D1*t4
t9 = t1**2
v2rhoa2(i) = -0.4135669939329333D0/t9
t12 = t4**2
v2rhob2(i) = -0.4135669939329333D0/t12
v2rhoab(i) = 0.D0
endif ! rhoa,rhob
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
vrhob(i) = 0.0d0
v2rhoa2(i) = 0.0d0
v2rhob2(i) = 0.0d0
v2rhoab(i) = 0.0d0
endif ! rho
enddo
endif ! ideriv
return
end
subroutine rks_x_lda
& (ideriv,npt,rhoa1,sigmaaa1,
& zk,vrhoa,vsigmaaa,
& v2rhoa2,v2rhoasigmaaa,v2sigmaaa2)
c
c P.A.M. Dirac
c Proceedings of the Cambridge Philosophical Society, 26 (1930) 376
c
c
c CITATION:
c
c Functionals were obtained from the Density Functional Repository
c as developed and distributed by the Quantum Chemistry Group,
c CCLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD
c United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or
c Paul Sherwood for further information.
c
c COPYRIGHT:
c
c Users may incorporate the source code into software packages and
c redistribute the source code provided the source code is not
c changed in anyway and is properly cited in any documentation or
c publication related to its use.
c
c ACKNOWLEDGEMENT:
c
c The source code was generated using Maple 8 through a modified
c version of the dfauto script published in:
c
c R. Strange, F.R. Manby, P.J. Knowles
c Automatic code generation in density functional theory
c Comp. Phys. Comm. 136 (2001) 310-318.
c
implicit real*8 (a-h,o-z)
integer ideriv,npt
real*8 rhoa1(npt)
real*8 sigmaaa1(npt)
real*8 zk(npt),vrhoa(npt),vsigmaaa(npt)
real*8 v2rhoa2(npt),v2rhoasigmaaa(npt),v2sigmaaa2(npt)
parameter(tol=1.0d-20)
if(ideriv.eq.0) then
do i=1,npt
rho = dmax1(0.D0,rhoa1(i))
if(rho.gt.tol) then
t1 = rho**(1.D0/3.D0)
zk(i) = -0.7385587663820224D0*t1*rho
else ! rho
zk(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.1) then
do i=1,npt
rho = dmax1(0.D0,rhoa1(i))
if(rho.gt.tol) then
t1 = rho**(1.D0/3.D0)
zk(i) = -0.7385587663820224D0*t1*rho
vrhoa(i) = -0.9847450218426965D0*t1
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.2) then
do i=1,npt
rho = dmax1(0.D0,rhoa1(i))
if(rho.gt.tol) then
t1 = rho**(1.D0/3.D0)
zk(i) = -0.7385587663820224D0*t1*rho
vrhoa(i) = -0.9847450218426965D0*t1
t5 = t1**2
v2rhoa2(i) = -0.6564966812284644D0/t5
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
v2rhoa2(i) = 0.0d0
endif ! rho
enddo
endif ! ideriv
return
end
subroutine uks_x_b88
& (ideriv,npt,rhoa1,rhob1,sigmaaa1,sigmabb1,sigmaab1,
& zk,vrhoa,vrhob,vsigmaaa,vsigmabb,vsigmaab,
& v2rhoa2,v2rhob2,v2rhoab,
& v2rhoasigmaaa,v2rhoasigmaab,v2rhoasigmabb,
& v2rhobsigmabb,v2rhobsigmaab,v2rhobsigmaaa,
& v2sigmaaa2,v2sigmaaaab,v2sigmaaabb,
& v2sigmaab2,v2sigmaabbb,v2sigmabb2)
c
c A.D. Becke
c Density-functional exchange-energy approximation with correct
c asymptotic behaviour
c Phys. Rev. A38 (1988) 3098-3100
c
c
c CITATION:
c
c Functionals were obtained from the Density Functional Repository
c as developed and distributed by the Quantum Chemistry Group,
c CCLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD
c United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or
c Paul Sherwood for further information.
c
c COPYRIGHT:
c
c Users may incorporate the source code into software packages and
c redistribute the source code provided the source code is not
c changed in anyway and is properly cited in any documentation or
c publication related to its use.
c
c ACKNOWLEDGEMENT:
c
c The source code was generated using Maple 8 through a modified
c version of the dfauto script published in:
c
c R. Strange, F.R. Manby, P.J. Knowles
c Automatic code generation in density functional theory
c Comp. Phys. Comm. 136 (2001) 310-318.
c
implicit real*8 (a-h,o-z)
integer ideriv,npt
real*8 rhoa1(npt),rhob1(npt)
real*8 sigmaaa1(npt),sigmabb1(npt),sigmaab1(npt)
real*8 zk(npt),vrhoa(npt),vrhob(npt)
real*8 vsigmaaa(npt),vsigmabb(npt),vsigmaab(npt)
real*8 v2rhoa2(npt),v2rhob2(npt),v2rhoab(npt)
real*8 v2rhoasigmaaa(npt),v2rhoasigmaab(npt)
real*8 v2rhoasigmabb(npt),v2rhobsigmabb(npt)
real*8 v2rhobsigmaab(npt),v2rhobsigmaaa(npt)
real*8 v2sigmaaa2(npt),v2sigmaaaab(npt),v2sigmaaabb(npt)
real*8 v2sigmaab2(npt),v2sigmaabbb(npt),v2sigmabb2(npt)
parameter(tol=1.0d-20)
if (ideriv.eq.0) then
do i=1,npt
rhoa = dmax1(0.D0,rhoa1(i))
rhob = dmax1(0.D0,rhob1(i))
rho = rhoa+rhob
if(rho.gt.tol) then
if(rhoa.lt.tol) then
rho = rhob
sigmabb = dmax1(0.D0,sigmabb1(i))
sigma = sigmabb
t2 = rhob**(1.D0/3.D0)
t3 = t2*rhob
t5 = 1/t3
t7 = dsqrt(sigmabb)
t8 = t7*t5
t9 = dlog(t8+dsqrt(1+t8**2))
zk(i) = -0.9305257363491D0*t3-0.42D-2*t5*sigmabb/(1.D0+0.252D-1
#*t8*t9)
elseif(rhob.lt.tol) then
rho = rhoa
sigmaaa = dmax1(0.D0,sigmaaa1(i))
sigma = sigmaaa
t2 = rhoa**(1.D0/3.D0)
t3 = t2*rhoa
t5 = 1/t3
t7 = dsqrt(sigmaaa)
t8 = t7*t5
t9 = dlog(t8+dsqrt(1+t8**2))
zk(i) = -0.9305257363491D0*t3-0.42D-2*t5*sigmaaa/(1.D0+0.252D-1
#*t8*t9)
else ! (.not.(rhoa.lt.tol).and..not.(rhob.lt.tol))
sigmaaa = dmax1(0.D0,sigmaaa1(i))
sigmaab = sigmaab1(i)
sigmabb = dmax1(0.D0,sigmabb1(i))
sigma = sigmaaa+sigmabb+2.D0*sigmaab
t4 = rhoa**(1.D0/3.D0)
t5 = t4*rhoa
t7 = 1/t5
t9 = dsqrt(sigmaaa)
t10 = t9*t7
t11 = dlog(t10+dsqrt(1+t10**2))
t18 = rhob**(1.D0/3.D0)
t19 = t18*rhob
t21 = 1/t19
t23 = dsqrt(sigmabb)
t24 = t23*t21
t25 = dlog(t24+dsqrt(1+t24**2))
zk(i) = -0.9305257363491D0*t5-0.42D-2*t7*sigmaaa/(1.D0+0.252D-1
#*t10*t11)-0.9305257363491D0*t19-0.42D-2*t21*sigmabb/(1.D0
#+0.252D-1*t24*t25)
endif ! rhoa,rhob
else ! rho
zk(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.1) then
do i=1,npt
rhoa = dmax1(0.D0,rhoa1(i))
rhob = dmax1(0.D0,rhob1(i))
rho = rhoa+rhob
if(rho.gt.tol) then
if(rhoa.lt.tol) then
rho = rhob
sigmabb = dmax1(0.D0,sigmabb1(i))
sigma = sigmabb
t2 = rhob**(1.D0/3.D0)
t3 = t2*rhob
t5 = 1/t3
t6 = t5*sigmabb
t7 = dsqrt(sigmabb)
t8 = t7*t5
t9 = dlog(t8+dsqrt(1+t8**2))
t12 = 1.D0+0.252D-1*t8*t9
t13 = 1/t12
zk(i) = -0.9305257363491D0*t3-0.42D-2*t6*t13
vrhoa(i) = 0.D0
t17 = rhob**2
t19 = 1/t2/t17
t23 = t12**2
t24 = 1/t23
t29 = t2**2
t34 = 1/t29/t17
t37 = dsqrt(1.D0+sigmabb*t34)
t38 = 1/t37
vrhob(i) = -0.12407009817988D1*t2+0.56D-2*t19*sigmabb*t13
#+0.42D-2*t6*t24*(-0.336D-1*t7*t19*t9-0.336D-1*sigmabb/t29/t17
#/rhob*t38)
vsigmaaa(i) = 0.D0
vsigmaab(i) = 0.D0
vsigmabb(i) = -0.42D-2*t5*t13+0.42D-2*t6*t24*(0.126D-1/t7*t5*t9
#+0.126D-1*t34*t38)
elseif(rhob.lt.tol) then
rho = rhoa
sigmaaa = dmax1(0.D0,sigmaaa1(i))
sigma = sigmaaa
t2 = rhoa**(1.D0/3.D0)
t3 = t2*rhoa
t5 = 1/t3
t6 = t5*sigmaaa
t7 = dsqrt(sigmaaa)
t8 = t7*t5
t9 = dlog(t8+dsqrt(1+t8**2))
t12 = 1.D0+0.252D-1*t8*t9
t13 = 1/t12
zk(i) = -0.9305257363491D0*t3-0.42D-2*t6*t13
t17 = rhoa**2
t19 = 1/t2/t17
t23 = t12**2
t24 = 1/t23
t29 = t2**2
t34 = 1/t29/t17
t37 = dsqrt(1.D0+sigmaaa*t34)
t38 = 1/t37
vrhoa(i) = -0.12407009817988D1*t2+0.56D-2*t19*sigmaaa*t13
#+0.42D-2*t6*t24*(-0.336D-1*t7*t19*t9-0.336D-1*sigmaaa/t29/t17
#/rhoa*t38)
vrhob(i) = 0.D0
vsigmaaa(i) = -0.42D-2*t5*t13+0.42D-2*t6*t24*(0.126D-1/t7*t5*t9
#+0.126D-1*t34*t38)
vsigmaab(i) = 0.D0
vsigmabb(i) = 0.D0
else ! (.not.(rhoa.lt.tol).and..not.(rhob.lt.tol))
sigmaaa = dmax1(0.D0,sigmaaa1(i))
sigmaab = sigmaab1(i)
sigmabb = dmax1(0.D0,sigmabb1(i))
sigma = sigmaaa+sigmabb+2.D0*sigmaab
t4 = rhoa**(1.D0/3.D0)
t5 = t4*rhoa
t7 = 1/t5
t8 = t7*sigmaaa
t9 = dsqrt(sigmaaa)
t10 = t9*t7
t11 = dlog(t10+dsqrt(1+t10**2))
t14 = 1.D0+0.252D-1*t10*t11
t15 = 1/t14
t18 = rhob**(1.D0/3.D0)
t19 = t18*rhob
t21 = 1/t19
t22 = t21*sigmabb
t23 = dsqrt(sigmabb)
t24 = t23*t21
t25 = dlog(t24+dsqrt(1+t24**2))
t28 = 1.D0+0.252D-1*t24*t25
t29 = 1/t28
zk(i) = -0.9305257363491D0*t5-0.42D-2*t8*t15-0.9305257363491D0
#*t19-0.42D-2*t22*t29
t33 = rhoa**2
t35 = 1/t4/t33
t39 = t14**2
t40 = 1/t39
t45 = t4**2
t50 = 1/t45/t33
t53 = dsqrt(1.D0+sigmaaa*t50)
t54 = 1/t53
vrhoa(i) = -0.12407009817988D1*t4+0.56D-2*t35*sigmaaa*t15
#+0.42D-2*t8*t40*(-0.336D-1*t9*t35*t11-0.336D-1*sigmaaa/t45/t33
#/rhoa*t54)
t62 = rhob**2
t64 = 1/t18/t62
t68 = t28**2
t69 = 1/t68
t74 = t18**2
t79 = 1/t74/t62
t82 = dsqrt(1.D0+sigmabb*t79)
t83 = 1/t82
vrhob(i) = -0.12407009817988D1*t18+0.56D-2*t64*sigmabb*t29
#+0.42D-2*t22*t69*(-0.336D-1*t23*t64*t25-0.336D-1*sigmabb/t74/t62
#/rhob*t83)
vsigmaaa(i) = -0.42D-2*t7*t15+0.42D-2*t8*t40*(0.126D-1/t9*t7*t11
#+0.126D-1*t50*t54)
vsigmaab(i) = 0.D0
vsigmabb(i) = -0.42D-2*t21*t29+0.42D-2*t22*t69*(0.126D-1/t23*t21
#*t25+0.126D-1*t79*t83)
endif ! rhoa,rhob
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
vrhob(i) = 0.0d0
vsigmaaa(i) = 0.0d0
vsigmaab(i) = 0.0d0
vsigmabb(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.2) then
do i=1,npt
rhoa = dmax1(0.D0,rhoa1(i))
rhob = dmax1(0.D0,rhob1(i))
rho = rhoa+rhob
if(rho.gt.tol) then
if(rhoa.lt.tol) then
rho = rhob
sigmabb = dmax1(0.D0,sigmabb1(i))
sigma = sigmabb
t2 = rhob**(1.D0/3.D0)
t3 = t2*rhob
t5 = 1/t3
t6 = t5*sigmabb
t7 = dsqrt(sigmabb)
t8 = t7*t5
t9 = dlog(t8+dsqrt(1+t8**2))
t12 = 1.D0+0.252D-1*t8*t9
t13 = 1/t12
zk(i) = -0.9305257363491D0*t3-0.42D-2*t6*t13
vrhoa(i) = 0.D0
t17 = rhob**2
t19 = 1/t2/t17
t20 = t19*sigmabb
t23 = t12**2
t24 = 1/t23
t28 = t17*rhob
t29 = t2**2
t34 = 1/t29/t17
t36 = 1.D0+sigmabb*t34
t37 = dsqrt(t36)
t38 = 1/t37
t41 = -0.336D-1*t7*t19*t9-0.336D-1*sigmabb/t29/t28*t38
t42 = t24*t41
vrhob(i) = -0.12407009817988D1*t2+0.56D-2*t20*t13+0.42D-2*t6*t42
vsigmaaa(i) = 0.D0
vsigmaab(i) = 0.D0
t53 = 0.126D-1/t7*t5*t9+0.126D-1*t34*t38
vsigmabb(i) = -0.42D-2*t5*t13+0.42D-2*t6*t24*t53
v2rhoa2(i) = 0.D0
v2rhoab(i) = 0.D0
t60 = 1/t2/t28
t67 = 1/t23/t12
t68 = t41**2
t75 = t17**2
t81 = sigmabb**2
t87 = 1/t37/t36
v2rhob2(i) = -0.4135669939329333D0/t29-0.1306666666666667D-1*t60
#*sigmabb*t13-0.112D-1*t20*t42-0.84D-2*t6*t67*t68+0.42D-2*t6*t24*
#(0.784D-1*t7*t60*t9+0.168D0*sigmabb/t29/t75*t38-0.448D-1*t81/t2
#/t75/t28*t87)
v2sigmaaa2(i) = 0.D0
v2sigmaaaab(i) = 0.D0
v2sigmaaabb(i) = 0.D0
v2sigmaab2(i) = 0.D0
v2sigmaabbb(i) = 0.D0
t97 = t53**2
v2sigmabb2(i) = 0.84D-2*t5*t24*t53-0.84D-2*t6*t67*t97+0.42D-2*t6
#*t24*(-0.63D-2/t7/sigmabb*t5*t9+0.63D-2/sigmabb*t34*t38-0.63D-2
#/t2/t75/rhob*t87)
elseif(rhob.lt.tol) then
rho = rhoa
sigmaaa = dmax1(0.D0,sigmaaa1(i))
sigma = sigmaaa
t2 = rhoa**(1.D0/3.D0)
t3 = t2*rhoa
t5 = 1/t3
t6 = t5*sigmaaa
t7 = dsqrt(sigmaaa)
t8 = t7*t5
t9 = dlog(t8+dsqrt(1+t8**2))
t12 = 1.D0+0.252D-1*t8*t9
t13 = 1/t12
zk(i) = -0.9305257363491D0*t3-0.42D-2*t6*t13
t17 = rhoa**2
t19 = 1/t2/t17
t20 = t19*sigmaaa
t23 = t12**2
t24 = 1/t23
t28 = t17*rhoa
t29 = t2**2
t34 = 1/t29/t17
t36 = 1.D0+sigmaaa*t34
t37 = dsqrt(t36)
t38 = 1/t37
t41 = -0.336D-1*t7*t19*t9-0.336D-1*sigmaaa/t29/t28*t38
t42 = t24*t41
vrhoa(i) = -0.12407009817988D1*t2+0.56D-2*t20*t13+0.42D-2*t6*t42
vrhob(i) = 0.D0
t53 = 0.126D-1/t7*t5*t9+0.126D-1*t34*t38
vsigmaaa(i) = -0.42D-2*t5*t13+0.42D-2*t6*t24*t53
vsigmaab(i) = 0.D0
vsigmabb(i) = 0.D0
t60 = 1/t2/t28
t67 = 1/t23/t12
t68 = t41**2
t75 = t17**2
t81 = sigmaaa**2
t87 = 1/t37/t36
v2rhoa2(i) = -0.4135669939329333D0/t29-0.1306666666666667D-1*t60
#*sigmaaa*t13-0.112D-1*t20*t42-0.84D-2*t6*t67*t68+0.42D-2*t6*t24*
#(0.784D-1*t7*t60*t9+0.168D0*sigmaaa/t29/t75*t38-0.448D-1*t81/t2
#/t75/t28*t87)
v2rhob2(i) = 0.D0
v2rhoab(i) = 0.D0
t97 = t53**2
v2sigmaaa2(i) = 0.84D-2*t5*t24*t53-0.84D-2*t6*t67*t97+0.42D-2*t6
#*t24*(-0.63D-2/t7/sigmaaa*t5*t9+0.63D-2/sigmaaa*t34*t38-0.63D-2
#/t2/t75/rhoa*t87)
v2sigmaaaab(i) = 0.D0
v2sigmaaabb(i) = 0.D0
v2sigmaab2(i) = 0.D0
v2sigmaabbb(i) = 0.D0
v2sigmabb2(i) = 0.D0
else ! (.not.(rhoa.lt.tol).and..not.(rhob.lt.tol))
sigmaaa = dmax1(0.D0,sigmaaa1(i))
sigmaab = sigmaab1(i)
sigmabb = dmax1(0.D0,sigmabb1(i))
sigma = sigmaaa+sigmabb+2.D0*sigmaab
t4 = rhoa**(1.D0/3.D0)
t5 = t4*rhoa
t7 = 1/t5
t8 = t7*sigmaaa
t9 = dsqrt(sigmaaa)
t10 = t9*t7
t11 = dlog(t10+dsqrt(1+t10**2))
t14 = 1.D0+0.252D-1*t10*t11
t15 = 1/t14
t18 = rhob**(1.D0/3.D0)
t19 = t18*rhob
t21 = 1/t19
t22 = t21*sigmabb
t23 = dsqrt(sigmabb)
t24 = t23*t21
t25 = dlog(t24+dsqrt(1+t24**2))
t28 = 1.D0+0.252D-1*t24*t25
t29 = 1/t28
zk(i) = -0.9305257363491D0*t5-0.42D-2*t8*t15-0.9305257363491D0
#*t19-0.42D-2*t22*t29
t33 = rhoa**2
t35 = 1/t4/t33
t36 = t35*sigmaaa
t39 = t14**2
t40 = 1/t39
t44 = t33*rhoa
t45 = t4**2
t47 = 1/t45/t44
t50 = 1/t45/t33
t52 = 1.D0+sigmaaa*t50
t53 = dsqrt(t52)
t54 = 1/t53
t57 = -0.336D-1*t9*t35*t11-0.336D-1*sigmaaa*t47*t54
t58 = t40*t57
vrhoa(i) = -0.12407009817988D1*t4+0.56D-2*t36*t15+0.42D-2*t8*t58
t62 = rhob**2
t64 = 1/t18/t62
t65 = t64*sigmabb
t68 = t28**2
t69 = 1/t68
t73 = t62*rhob
t74 = t18**2
t76 = 1/t74/t73
t79 = 1/t74/t62
t81 = 1.D0+sigmabb*t79
t82 = dsqrt(t81)
t83 = 1/t82
t86 = -0.336D-1*t23*t64*t25-0.336D-1*sigmabb*t76*t83
t87 = t69*t86
vrhob(i) = -0.12407009817988D1*t18+0.56D-2*t65*t29+0.42D-2*t22*t87
t92 = 1/t9
t98 = 0.126D-1*t92*t7*t11+0.126D-1*t50*t54
t99 = t40*t98
vsigmaaa(i) = -0.42D-2*t7*t15+0.42D-2*t8*t99
vsigmaab(i) = 0.D0
t104 = 1/t23
t110 = 0.126D-1*t104*t21*t25+0.126D-1*t79*t83
t111 = t69*t110
vsigmabb(i) = -0.42D-2*t21*t29+0.42D-2*t22*t111
t117 = 1/t4/t44
t124 = 1/t39/t14
t125 = t57**2
t132 = t33**2
t138 = sigmaaa**2
t144 = 1/t53/t52
v2rhoa2(i) = -0.4135669939329333D0/t45-0.1306666666666667D-1
#*t117*sigmaaa*t15-0.112D-1*t36*t58-0.84D-2*t8*t124*t125+0.42D-2
#*t8*t40*(0.784D-1*t9*t117*t11+0.168D0*sigmaaa/t45/t132*t54
#-0.448D-1*t138/t4/t132/t44*t144)
t154 = 1/t18/t73
t161 = 1/t68/t28
t162 = t86**2
t169 = t62**2
t175 = sigmabb**2
t181 = 1/t82/t81
v2rhob2(i) = -0.4135669939329333D0/t74-0.1306666666666667D-1
#*t154*sigmabb*t29-0.112D-1*t65*t87-0.84D-2*t22*t161*t162+0.42D-2
#*t22*t69*(0.784D-1*t23*t154*t25+0.168D0*sigmabb/t74/t169*t83
#-0.448D-1*t175/t18/t169/t73*t181)
v2rhoab(i) = 0.D0
t192 = t7*t40
v2rhoasigmaaa(i) = 0.56D-2*t35*t15-0.56D-2*t36*t99+0.42D-2*t192
#*t57-0.84D-2*t8*t124*t57*t98+0.42D-2*t8*t40*(-0.168D-1*t92*t35
#*t11-0.504D-1*t47*t54+0.168D-1*sigmaaa/t4/t132/t33*t144)
v2rhoasigmaab(i) = 0.D0
v2rhoasigmabb(i) = 0.D0
v2rhobsigmaaa(i) = 0.D0
v2rhobsigmaab(i) = 0.D0
t218 = t21*t69
v2rhobsigmabb(i) = 0.56D-2*t64*t29-0.56D-2*t65*t111+0.42D-2*t218
#*t86-0.84D-2*t22*t161*t86*t110+0.42D-2*t22*t69*(-0.168D-1*t104
#*t64*t25-0.504D-1*t76*t83+0.168D-1*sigmabb/t18/t169/t62*t181)
t242 = t98**2
v2sigmaaa2(i) = 0.84D-2*t192*t98-0.84D-2*t8*t124*t242+0.42D-2*t8
#*t40*(-0.63D-2/t9/sigmaaa*t7*t11+0.63D-2/sigmaaa*t50*t54-0.63D-2
#/t4/t132/rhoa*t144)
v2sigmaaaab(i) = 0.D0
v2sigmaaabb(i) = 0.D0
v2sigmaab2(i) = 0.D0
v2sigmaabbb(i) = 0.D0
t266 = t110**2
v2sigmabb2(i) = 0.84D-2*t218*t110-0.84D-2*t22*t161*t266+0.42D-2
#*t22*t69*(-0.63D-2/t23/sigmabb*t21*t25+0.63D-2/sigmabb*t79*t83
#-0.63D-2/t18/t169/rhob*t181)
endif ! rhoa,rhob
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
vrhob(i) = 0.0d0
v2rhoa2(i) = 0.0d0
v2rhob2(i) = 0.0d0
v2rhoab(i) = 0.0d0
vsigmaaa(i) = 0.0d0
vsigmaab(i) = 0.0d0
vsigmabb(i) = 0.0d0
v2rhoasigmaaa(i) = 0.0d0
v2rhoasigmaab(i) = 0.0d0
v2rhoasigmabb(i) = 0.0d0
v2rhobsigmaaa(i) = 0.0d0
v2rhobsigmaab(i) = 0.0d0
v2rhobsigmabb(i) = 0.0d0
v2sigmaaa2(i) = 0.0d0
v2sigmaab2(i) = 0.0d0
v2sigmabb2(i) = 0.0d0
v2sigmaaaab(i) = 0.0d0
v2sigmaaabb(i) = 0.0d0
v2sigmaabbb(i) = 0.0d0
endif ! rho
enddo
endif ! ideriv
return
end
subroutine rks_x_b88
& (ideriv,npt,rhoa1,sigmaaa1,
& zk,vrhoa,vsigmaaa,
& v2rhoa2,v2rhoasigmaaa,v2sigmaaa2)
c
c A.D. Becke
c Density-functional exchange-energy approximation with correct
c asymptotic behaviour
c Phys. Rev. A38 (1988) 3098-3100
c
c
c CITATION:
c
c Functionals were obtained from the Density Functional Repository
c as developed and distributed by the Quantum Chemistry Group,
c CCLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD
c United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or
c Paul Sherwood for further information.
c
c COPYRIGHT:
c
c Users may incorporate the source code into software packages and
c redistribute the source code provided the source code is not
c changed in anyway and is properly cited in any documentation or
c publication related to its use.
c
c ACKNOWLEDGEMENT:
c
c The source code was generated using Maple 8 through a modified
c version of the dfauto script published in:
c
c R. Strange, F.R. Manby, P.J. Knowles
c Automatic code generation in density functional theory
c Comp. Phys. Comm. 136 (2001) 310-318.
c
implicit real*8 (a-h,o-z)
integer ideriv,npt
real*8 rhoa1(npt)
real*8 sigmaaa1(npt)
real*8 zk(npt),vrhoa(npt),vsigmaaa(npt)
real*8 v2rhoa2(npt),v2rhoasigmaaa(npt),v2sigmaaa2(npt)
parameter(tol=1.0d-20)
if(ideriv.eq.0) then
do i=1,npt
rho = dmax1(0.D0,rhoa1(i))
if(rho.gt.tol) then
sigma = dmax1(0.D0,sigmaaa1(i))
t2 = rho**(1.D0/3.D0)
t3 = t2*rho
t5 = 1/t3
t7 = dsqrt(sigma)
t8 = t7*t5
t10 = dlog(0.1259921049894873D1*t8+dsqrt(1+0.1587401051968199D1
#*t8**2))
zk(i) = -0.7385587663820224D0*t3-0.5291668409558467D-2*t5*sigma/
#(1.D0+0.317500104573508D-1*t8*t10)
else ! rho
zk(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.1) then
do i=1,npt
rho = dmax1(0.D0,rhoa1(i))
if(rho.gt.tol) then
sigma = dmax1(0.D0,sigmaaa1(i))
t2 = rho**(1.D0/3.D0)
t3 = t2*rho
t5 = 1/t3
t6 = t5*sigma
t7 = dsqrt(sigma)
t8 = t7*t5
t10 = dlog(0.1259921049894873D1*t8+dsqrt(1+0.1587401051968199D1
#*t8**2))
t13 = 1.D0+0.317500104573508D-1*t8*t10
t14 = 1/t13
zk(i) = -0.7385587663820224D0*t3-0.5291668409558467D-2*t6*t14
t18 = rho**2
t20 = 1/t2/t18
t24 = t13**2
t25 = 1/t24
t30 = t2**2
t35 = 1/t30/t18
t39 = dsqrt(1.D0+0.1587401051968199D1*sigma*t35)
t40 = 1/t39
vrhoa(i) = -0.9847450218426965D0*t2+0.705555787941129D-2*t20
#*sigma*t14+0.2645834204779234D-2*t6*t25*(-0.8466669455293548D-1
#*t7*t20*t10-0.106673350692263D0*sigma/t30/t18/rho*t40)
vsigmaaa(i) = -0.2116667363823387D-1*t5*t14
#+0.5291668409558467D-2*t6*t25*(0.6350002091470161D-1/t7*t5*t10
#+0.8000501301919725D-1*t35*t40)
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
vsigmaaa(i) = 0.0d0
endif ! rho
enddo
else if(ideriv.eq.2) then
do i=1,npt
rho = dmax1(0.D0,rhoa1(i))
if(rho.gt.tol) then
sigma = dmax1(0.D0,sigmaaa1(i))
t2 = rho**(1.D0/3.D0)
t3 = t2*rho
t5 = 1/t3
t6 = t5*sigma
t7 = dsqrt(sigma)
t8 = t7*t5
t10 = dlog(0.1259921049894873D1*t8+dsqrt(1+0.1587401051968199D1
#*t8**2))
t13 = 1.D0+0.317500104573508D-1*t8*t10
t14 = 1/t13
zk(i) = -0.7385587663820224D0*t3-0.5291668409558467D-2*t6*t14
t18 = rho**2
t20 = 1/t2/t18
t21 = t20*sigma
t24 = t13**2
t25 = 1/t24
t29 = t18*rho
t30 = t2**2
t32 = 1/t30/t29
t35 = 1/t30/t18
t38 = 1.D0+0.1587401051968199D1*sigma*t35
t39 = dsqrt(t38)
t40 = 1/t39
t43 = -0.8466669455293548D-1*t7*t20*t10-0.106673350692263D0
#*sigma*t32*t40
t44 = t25*t43
vrhoa(i) = -0.9847450218426965D0*t2+0.705555787941129D-2*t21*t14
#+0.2645834204779234D-2*t6*t44
t49 = 1/t7
t55 = 0.6350002091470161D-1*t49*t5*t10+0.8000501301919725D-1*t35
#*t40
t56 = t25*t55
vsigmaaa(i) = -0.2116667363823387D-1*t5*t14
#+0.5291668409558467D-2*t6*t56
t62 = 1/t2/t29
t69 = 1/t24/t13
t70 = t43**2
t77 = t18**2
t83 = sigma**2
t89 = 1/t39/t38
v2rhoa2(i) = -0.6564966812284644D0/t30-0.3292593677058602D-1*t62
#*sigma*t14-0.1411111575882258D-1*t21*t44-0.5291668409558467D-2
#*t6*t69*t70+0.2645834204779234D-2*t6*t25*(0.3951112412470322D0
#*t7*t62*t10+0.106673350692263D1*sigma/t30/t77*t40
#-0.4515557042823225D0*t83/t2/t77/t29*t89)
t100 = t5*t25
v2rhoasigmaaa(i) = 0.2822223151764516D-1*t20*t14
#-0.705555787941129D-2*t21*t56+0.1058333681911693D-1*t100*t43
#-0.5291668409558467D-2*t6*t69*t43*t55+0.2645834204779234D-2*t6
#*t25*(-0.169333389105871D0*t49*t20*t10-0.640040104153578D0*t32
#*t40+0.3386667782117419D0*sigma/t2/t77/t18*t89)
t124 = t55**2
v2sigmaaa2(i) = 0.4233334727646774D-1*t100*t55
#-0.1058333681911693D-1*t6*t69*t124+0.5291668409558467D-2*t6*t25*
#(-0.1270000418294032D0/t7/sigma*t5*t10+0.1600100260383945D0
#/sigma*t35*t40-0.2540000836588064D0/t2/t77/rho*t89)
else ! rho
zk(i) = 0.0d0
vrhoa(i) = 0.0d0
v2rhoa2(i) = 0.0d0
vsigmaaa(i) = 0.0d0
v2rhoasigmaaa(i) = 0.0d0
v2sigmaaa2(i) = 0.0d0
endif ! rho
enddo
endif ! ideriv
return
end
subroutine uks_x_pbe
& (ideriv,npt,rhoa1,rhob1,sigmaaa1,sigmabb1,sigmaab1,
& zk,vrhoa,vrhob,vsigmaaa,vsigmabb,vsigmaab,
& v2rhoa2,v2rhob2,v2rhoab,
& v2rhoasigmaaa,v2rhoasigmaab,v2rhoasigmabb,
& v2rhobsigmabb,v2rhobsigmaab,v2rhobsigmaaa,
& v2sigmaaa2,v2sigmaaaab,v2sigmaaabb,
& v2sigmaab2,v2sigmaabbb,v2sigmabb2)
c
c J.P. Perdew, K. Burke, and M. Ernzerhof
c Generalized gradient approximation made simple
c Phys. Rev. Lett. 77 (1996) 3865-3868
c
c
c CITATION:
c
c Functionals were obtained from the Density Functional Repository
c as developed and distributed by the Quantum Chemistry Group,
c CCLRC Daresbury Laboratory, Daresbury, Cheshire, WA4 4AD
c United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or
c Paul Sherwood for further information.
c
c COPYRIGHT:
c
c Users may incorporate the source code into software packages and
c redistribute the source code provided the source code is not
c changed in anyway and is properly cited in any documentation or
c publication related to its use.
c
c ACKNOWLEDGEMENT:
c
c The source code was generated using Maple 8 through a modified
c version of the dfauto script published in:
c
c R. Strange, F.R. Manby, P.J. Knowles
c Automatic code generation in density functional theory
c Comp. Phys. Comm. 136 (2001) 310-318.
c