265 lines
7.7 KiB
Fortran
265 lines
7.7 KiB
Fortran
|
|
subroutine give_all_stuffs_in_r_for_lyp_88(r,rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2)
|
|
implicit none
|
|
double precision, intent(in) :: r(3)
|
|
double precision, intent(out) :: rho_a(N_states),rho_b(N_states),grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_2(N_states),rho(N_states)
|
|
double precision :: grad_rho_a(3,N_states),grad_rho_b(3,N_states),grad_rho_a_b(N_states)
|
|
double precision :: grad_aos_array(3,ao_num),aos_array(ao_num)
|
|
|
|
call density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r(r,rho_a,rho_b, grad_rho_a, grad_rho_b, aos_array, grad_aos_array)
|
|
integer :: i,istate
|
|
rho = rho_a + rho_b
|
|
grad_rho_a_2 = 0.d0
|
|
grad_rho_b_2 = 0.d0
|
|
grad_rho_a_b = 0.d0
|
|
do istate = 1, N_states
|
|
do i = 1, 3
|
|
grad_rho_a_2(istate) += grad_rho_a(i,istate) * grad_rho_a(i,istate)
|
|
grad_rho_b_2(istate) += grad_rho_b(i,istate) * grad_rho_b(i,istate)
|
|
grad_rho_a_b(istate) += grad_rho_a(i,istate) * grad_rho_b(i,istate)
|
|
enddo
|
|
enddo
|
|
grad_rho_2 = grad_rho_a_2 + grad_rho_b_2 + 2.d0 * grad_rho_a_b
|
|
|
|
end
|
|
|
|
|
|
double precision function ec_lyp_88(rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2)
|
|
|
|
implicit none
|
|
|
|
BEGIN_DOC
|
|
! LYP functional of the Lee, Yan, Parr, Phys. Rev B 1988, Vol 37, page 785.
|
|
! The expression used is the one by Miehlich, Savin, Stoll, Preuss, CPL, 1989 which gets rid of the laplacian of the density
|
|
END_DOC
|
|
|
|
include 'constants.include.F'
|
|
|
|
! Input variables
|
|
double precision, intent(in) :: rho,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_2
|
|
! Local variables
|
|
double precision :: a,b,c,d,c_f,omega,delta
|
|
double precision :: rho_13,rho_inv_13,rho_83,rho_113,rho_inv_113,denom
|
|
double precision :: thr,huge_num,rho_inv
|
|
double precision :: cst_2_113,cst_8_3,rho_2,rho_a_2,rho_b_2
|
|
double precision :: tmp1,tmp2,tmp3,tmp4
|
|
double precision :: big1,big2,big3
|
|
|
|
|
|
! Constants of the LYP correlation functional
|
|
|
|
a = 0.04918d0
|
|
b = 0.132d0
|
|
c = 0.2533d0
|
|
d = 0.349d0
|
|
|
|
ec_lyp_88 = 0.d0
|
|
|
|
thr = 1d-15
|
|
huge_num = 1.d0/thr
|
|
if(dabs(rho_a).lt.thr)then
|
|
return
|
|
endif
|
|
|
|
if(dabs(rho_b).lt.thr)then
|
|
return
|
|
endif
|
|
|
|
if(rho.lt.0.d0)then
|
|
print*,'pb !! rho.lt.0.d0'
|
|
stop
|
|
endif
|
|
|
|
rho_13 = rho**(1.d0/3.d0)
|
|
rho_113 = rho**(11.d0/3.d0)
|
|
|
|
if(dabs(rho_13) < thr) then
|
|
rho_inv_13 = huge_num
|
|
else
|
|
rho_inv_13 = 1.d0/rho_13
|
|
endif
|
|
|
|
if (dabs(rho_113) < thr) then
|
|
rho_inv_113 = huge_num
|
|
else
|
|
rho_inv_113 = 1.d0/rho_113
|
|
endif
|
|
|
|
if (dabs(rho) < thr) then
|
|
rho_inv = huge_num
|
|
else
|
|
rho_inv = 1.d0/rho
|
|
endif
|
|
|
|
! Useful quantities to predefine
|
|
|
|
denom = 1d0/(1d0 + d*rho_inv_13)
|
|
omega = rho_inv_113*exp(-c*rho_inv_13)*denom
|
|
delta = c*rho_inv_13 + d*rho_inv_13*denom
|
|
c_f = 0.3d0*(3.d0*pi*pi)**(2.d0/3.d0)
|
|
|
|
rho_2 = rho *rho
|
|
rho_a_2 = rho_a*rho_a
|
|
rho_b_2 = rho_b*rho_b
|
|
|
|
cst_2_113 = 2.d0**(11.d0/3.d0)
|
|
cst_8_3 = 8.d0/3.d0
|
|
|
|
! first term in the equation (2) of Preuss CPL, 1989
|
|
|
|
big1 = 4.d0*denom*rho_a*rho_b*rho_inv
|
|
|
|
tmp1 = cst_2_113*c_f*(rho_a**cst_8_3 + rho_b**cst_8_3)
|
|
tmp2 = (47.d0/18.d0 - 7.d0/18.d0*delta)*grad_rho_2
|
|
tmp3 = - (5d0/2d0 - 1.d0/18d0*delta)*(grad_rho_a_2 + grad_rho_b_2)
|
|
tmp4 = - (delta - 11d0)/9d0*(rho_a*rho_inv*grad_rho_a_2 + rho_b*rho_inv*grad_rho_b_2)
|
|
big2 = rho_a*rho_b*(tmp1 + tmp2 + tmp3 + tmp4)
|
|
|
|
tmp1 = -2d0/3d0*rho_2*grad_rho_2
|
|
tmp2 = grad_rho_b_2*(2d0/3d0*rho_2 - rho_a_2)
|
|
tmp3 = grad_rho_a_2*(2d0/3d0*rho_2 - rho_b_2)
|
|
big3 = tmp1 + tmp2 + tmp3
|
|
|
|
ec_lyp_88 = -a*big1 -a*b*omega*big2 -a*b*omega*big3
|
|
|
|
end
|
|
|
|
double precision function ec_lyp2(RhoA,RhoB,GA,GB,GAB)
|
|
include 'constants.include.F'
|
|
implicit none
|
|
double precision, intent(in) :: RhoA,RhoB,GA,GB,GAB
|
|
double precision :: Tol,caa,cab,cac,cad,cae,RA,RB,comega,cdelta,cLaa,cLbb,cLab,E
|
|
ec_lyp2 = 0.d0
|
|
Tol=1D-14
|
|
E=2.718281828459045D0
|
|
caa=0.04918D0
|
|
cab=0.132D0
|
|
cac=0.2533D0
|
|
cad=0.349D0
|
|
cae=(2D0**(11D0/3D0))*((3D0/10D0)*((3D0*(Pi**2D0))**(2D0/3D0)))
|
|
|
|
|
|
RA = MAX(RhoA,0D0)
|
|
RB = MAX(RhoB,0D0)
|
|
IF ((RA.gt.Tol).OR.(RB.gt.Tol)) THEN
|
|
IF ((RA.gt.Tol).AND.(RB.gt.Tol)) THEN
|
|
comega = 1D0/(E**(cac/(RA+RB)**(1D0/3D0))*(RA+RB)**(10D0/3D0)*(cad+(RA+RB)**(1D0/3D0)))
|
|
cdelta = (cac+cad+(cac*cad)/(RA+RB)**(1D0/3D0))/(cad+(RA+RB)**(1D0/3D0))
|
|
cLaa = (cab*comega*RB*(RA-3D0*cdelta*RA-9D0*RB-((-11D0+cdelta)*RA**2D0)/(RA+RB)))/9D0
|
|
cLbb = (cab*comega*RA*(-9D0*RA+(RB*(RA-3D0*cdelta*RA-4D0*(-3D0+cdelta)*RB))/(RA+RB)))/9D0
|
|
cLab = cab*comega*(((47D0-7D0*cdelta)*RA*RB)/9D0-(4D0*(RA+RB)**2D0)/3D0)
|
|
ec_lyp2 = -(caa*(cLaa*GA+cLab*GAB+cLbb*GB+cab*cae*comega*RA*RB*(RA**(8D0/3D0)+RB**(8D0/3D0))+(4D0*RA*RB)/(RA+RB+cad*(RA+RB)**(2D0/3D0))))
|
|
endif
|
|
endif
|
|
end
|
|
|
|
double precision function ec_scan(rho_a,rho_b,tau,grad_rho_2)
|
|
include 'constants.include.F'
|
|
implicit none
|
|
double precision, intent(in) :: rho_a,rho_b,tau,grad_rho_2
|
|
double precision :: cst_13,cst_23,cst_43,cst_53,rho_inv,cst_18,cst_3pi2
|
|
double precision :: thr,nup,ndo,xi,s,spin_d,drho,drho2,rho,inv_1alph,e_c_lsda1,h0
|
|
double precision :: rs,t_w,t_unif,ds_xi,alpha,fc_alpha,step_f,cst_1alph,beta_inf
|
|
double precision :: c_1c,c_2c,d_c,e_c_ldsa1,h1,phi,t,beta_rs,gama,a,w_1,g_at2,phi_3,e_c_1
|
|
double precision :: b_1c,b_2c,b_3c,dx_xi,gc_xi,e_c_lsda0,w_0,g_inf,cx_xi,x_inf,f0,e_c_0
|
|
thr = 1.d-12
|
|
nup = max(rho_a,thr)
|
|
ndo = max(rho_b,thr)
|
|
rho = nup + ndo
|
|
ec_scan = 0.d0
|
|
if((rho).lt.thr)return
|
|
! constants ...
|
|
rho_inv = 1.d0/rho
|
|
cst_13 = 1.d0/3.d0
|
|
cst_23 = 2.d0 * cst_13
|
|
cst_43 = 4.d0 * cst_13
|
|
cst_53 = 5.d0 * cst_13
|
|
cst_18 = 1.d0/8.d0
|
|
cst_3pi2 = 3.d0 * pi*pi
|
|
drho2 = max(grad_rho_2,thr)
|
|
drho = dsqrt(drho2)
|
|
if((nup-ndo).gt.0.d0)then
|
|
spin_d = max(nup-ndo,thr)
|
|
else
|
|
spin_d = min(nup-ndo,-thr)
|
|
endif
|
|
c_1c = 0.64d0
|
|
c_2c = 1.5d0
|
|
d_c = 0.7d0
|
|
b_1c = 0.0285764d0
|
|
b_2c = 0.0889d0
|
|
b_3c = 0.125541d0
|
|
gama = 0.031091d0
|
|
! correlation energy lsda1
|
|
call ec_only_lda_sr(0.d0,nup,ndo,e_c_lsda1)
|
|
|
|
! correlation energy per particle
|
|
e_c_lsda1 = e_c_lsda1/rho
|
|
xi = spin_d/rho
|
|
rs = (cst_43 * pi * rho)**(-cst_13)
|
|
s = drho/( 2.d0 * cst_3pi2**(cst_13) * rho**cst_43 )
|
|
t_w = drho2 * cst_18 * rho_inv
|
|
ds_xi = 0.5d0 * ( (1.d0+xi)**cst_53 + (1.d0 - xi)**cst_53)
|
|
t_unif = 0.3d0 * (cst_3pi2)**cst_23 * rho**cst_53*ds_xi
|
|
t_unif = max(t_unif,thr)
|
|
alpha = (tau - t_w)/t_unif
|
|
cst_1alph= 1.d0 - alpha
|
|
if(cst_1alph.gt.0.d0)then
|
|
cst_1alph= max(cst_1alph,thr)
|
|
else
|
|
cst_1alph= min(cst_1alph,-thr)
|
|
endif
|
|
inv_1alph= 1.d0/cst_1alph
|
|
phi = 0.5d0 * ( (1.d0+xi)**cst_23 + (1.d0 - xi)**cst_23)
|
|
phi_3 = phi*phi*phi
|
|
t = (cst_3pi2/16.d0)**cst_13 * s / (phi * rs**0.5d0)
|
|
w_1 = dexp(-e_c_lsda1/(gama * phi_3)) - 1.d0
|
|
a = beta_rs(rs) /(gama * w_1)
|
|
g_at2 = 1.d0/(1.d0 + 4.d0 * a*t*t)**0.25d0
|
|
h1 = gama * phi_3 * dlog(1.d0 + w_1 * (1.d0 - g_at2))
|
|
! interpolation function
|
|
|
|
if(cst_1alph.gt.0.d0)then
|
|
fc_alpha = dexp(-c_1c * alpha * inv_1alph)
|
|
else
|
|
fc_alpha = - d_c * dexp(c_2c * inv_1alph)
|
|
endif
|
|
! first part of the correlation energy
|
|
e_c_1 = e_c_lsda1 + h1
|
|
|
|
dx_xi = 0.5d0 * ( (1.d0+xi)**cst_43 + (1.d0 - xi)**cst_43)
|
|
gc_xi = (1.d0 - 2.3631d0 * (dx_xi - 1.d0) ) * (1.d0 - xi**12.d0)
|
|
e_c_lsda0= - b_1c / (1.d0 + b_2c * rs**0.5d0 + b_3c * rs)
|
|
w_0 = dexp(-e_c_lsda0/b_1c) - 1.d0
|
|
beta_inf = 0.066725d0 * 0.1d0 / 0.1778d0
|
|
cx_xi = -3.d0/(4.d0*pi) * (9.d0 * pi/4.d0)**cst_13 * dx_xi
|
|
|
|
x_inf = 0.128026d0
|
|
f0 = -0.9d0
|
|
g_inf = 1.d0/(1.d0 + 4.d0 * x_inf * s*s)**0.25d0
|
|
|
|
h0 = b_1c * dlog(1.d0 + w_0 * (1.d0 - g_inf))
|
|
e_c_0 = (e_c_lsda0 + h0) * gc_xi
|
|
|
|
ec_scan = e_c_1 + fc_alpha * (e_c_0 - e_c_1)
|
|
end
|
|
|
|
|
|
double precision function beta_rs(rs)
|
|
implicit none
|
|
double precision, intent(in) ::rs
|
|
beta_rs = 0.066725d0 * (1.d0 + 0.1d0 * rs)/(1.d0 + 0.1778d0 * rs)
|
|
|
|
end
|
|
|
|
|
|
double precision function step_f(x)
|
|
implicit none
|
|
double precision, intent(in) :: x
|
|
if(x.lt.0.d0)then
|
|
step_f = 0.d0
|
|
else
|
|
step_f = 1.d0
|
|
endif
|
|
end
|