530 lines
15 KiB
Fortran
530 lines
15 KiB
Fortran
subroutine ec_pbe_sr(mu,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,ec,vrhoc,vrhoo,vsigmacc,vsigmaco,vsigmaoo)
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BEGIN_DOC
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! Short-range pbe correlation energy functional for erf interaction
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!
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! input : ==========
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!
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! mu = range separated parameter
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!
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! rhoc, rhoo = total density and spin density
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!
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! sigmacc = square of the gradient of the total density
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!
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! sigmaco = square of the gradient of the spin density
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!
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! sigmaoo = scalar product between the gradient of the total density and the one of the spin density
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!
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! output: ==========
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!
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! ec = correlation energy
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!
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! all variables v** are energy derivatives with respect to components of the density
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!
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! vrhoc = derivative with respect to the total density
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!
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! vrhoo = derivative with respect to spin density
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!
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! vsigmacc = derivative with respect to the square of the gradient of the total density
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!
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! vsigmaco = derivative with respect to scalar product between the gradients of total and spin densities
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!
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! vsigmaoo = derivative with respect to the square of the gradient of the psin density
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END_DOC
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include 'constants.include.F'
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implicit none
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double precision, intent(in) :: rhoc,rhoo,mu
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double precision, intent(in) :: sigmacc,sigmaco,sigmaoo
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double precision, intent(out) :: ec
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double precision, intent(out) :: vrhoc,vrhoo
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double precision, intent(out) :: vsigmacc,vsigmaco,vsigmaoo
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double precision tol
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parameter(tol=1d-12)
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character(len=30) namedummy
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double precision eccerflda
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double precision vrhoccerflda
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double precision vrhoocerflda
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double precision ecclda
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double precision vrhocclda
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double precision vrhooclda
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integer i,igrad
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double precision rho,drho2,rhoa,rhob
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double precision ecerflda,decerfldadrho
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double precision eclda,decldadrho
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double precision ecerfpbe,decerfpbedrho,decerfpbedrhoo
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double precision decerfpbeddrho2
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double precision arglog,arglogs,arglogss,alpha,beta,betas,gamma
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double precision Aa,Ab,Ac,Aas,tq,tqs,tqss,decerfpur,decpur
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double precision t1,t2,t3,t4,t5,t6,t7,t8,t9,t10
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double precision t11,t12,t13,t14,t15,t16,t17,t18,t19
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double precision zeta,phi,phi2,phi3,phi4,phis,arglogsc
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double precision dlogarglog
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double precision, parameter :: f13=0.333333333333333d0
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! Parameter of the modified interaction
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ec = 0.d0
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vrhoc = 0.d0
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vrhoo = 0.d0
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vsigmacc = 0.d0
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vsigmaco = 0.d0
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vsigmaoo = 0.d0
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! First-type gradient functional
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igrad=1
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alpha=2.78d0
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gamma=3.1091d-2
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! test on density
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if (dabs(rhoc).lt.tol) return
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double precision :: vc_a,vc_b
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! Spin polarisation
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rhoa=max((rhoc+rhoo)*.5d0,1.0d-15)
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rhob=max((rhoc-rhoo)*.5d0,1.0d-15)
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call ec_lda_sr(mu,rhoa,rhob,eccerflda,vc_a,vc_b)
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ecerflda = eccerflda
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vrhoccerflda = 0.5d0 * (vc_a + vc_b)
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vrhoocerflda = 0.5d0 * (vc_a - vc_b)
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! Density
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rho = rhoc
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! Square of density gradient
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drho2 = sigmacc
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zeta = (rhoa-rhob)/(rhoa+rhob)
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! lda energy density
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double precision :: vc_a_lda,vc_b_lda
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call ec_lda(rhoa,rhob,ecclda,vc_a_lda,vc_b_lda)
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eclda = ecclda
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if ((ecerflda/eclda).le.0d0) then
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beta=0d0
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else
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beta=6.6725d-2*(ecerflda/eclda)**alpha
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endif
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phi=((1d0+zeta)**(2d0/3d0)+(1d0-zeta)**(2d0/3d0))/2d0
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phi2=phi*phi
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phi3=phi2*phi
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phi4=phi3*phi
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tq=drho2*6.346820607d-2*rho**(-7d0/3d0)/phi2
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Ab=dexp(-ecerflda/(rho*gamma*phi3))-1d0
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if (dabs(Ab).le.dabs(beta*tol)) then
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ecerfpbe=ecerflda
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else
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Aa=beta/(gamma*Ab)
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Ac=1d0+Aa*tq+Aa**2*tq**2
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if (Aa.lt.tol) Aa=tol
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arglog=1d0+beta*(1d0-1d0/Ac)/(gamma*Aa)
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ecerfpbe=ecerflda+rho*phi3*gamma*dlog(arglog)
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end if
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ec = ecerfpbe
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! Derive
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! lda energy density derivative
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decerfldadrho = vrhoccerflda
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decldadrho = 0.5d0 * (vc_a_lda+vc_b_lda)
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decerfpur=(decerfldadrho-ecerflda/rho)/rho
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decpur=(decldadrho-eclda/rho)/rho
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betas=alpha*beta*(decerfpur*rho/ecerflda-decpur*rho/eclda)
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phis=((rhoa - rhob)*((rhoa/(rhoa + rhob))**f13 - (rhob/(rhoa + rhob))**f13))/(3d0*2d0**f13*(rhoa/(rhoa + rhob))**f13*(rhob/(rhoa + rhob))**f13*(rhoa + rhob)**2)
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if (dabs(Ab).le.dabs(beta*tol)) then
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decerfpbedrho=decerfldadrho
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else
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Aas=betas/(gamma*Ab)+Aa*(1d0+1d0/Ab)*(decerfpur/phi3-3d0*phis*ecerflda/(rho*phi4))/gamma
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tqs=-7d0*tq/(3d0*rho)-2d0*tq*phis/phi
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arglogs=betas*tq*(1d0+Aa*tq)/(Ac*gamma)+beta*tqs*(1d0+Aa*tq)/(Ac*gamma)-beta*tq*Aa*tq*(Aas*tq+Aa*tqs)*(2d0+Aa*tq)/(Ac**2*gamma)
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dlogarglog=dlog(arglog)
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decerfpbedrho=decerfldadrho+gamma*(phi3*dlogarglog+3d0*rho*phis*phi2*dlogarglog+rho*phi3*arglogs/arglog)
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end if
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if (dabs(Ab).le.dabs(beta*tol)) then
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decerfpbeddrho2=0.0d0
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else
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arglogsc=Ab*(Aa+2d0*Aa*Aa*tq)/(Ac*Ac)
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tqss=6.346820607d-2*rho**(-7d0/3d0)/phi2
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arglogss=tqss*arglogsc
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decerfpbeddrho2=rho*gamma*phi3*arglogss/arglog
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end if
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! lda energy density derivative
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decerfldadrho = vrhoocerflda
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decldadrho = 0.5d0 * (vc_a_lda-vc_b_lda)
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decerfpur=decerfldadrho/rho
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decpur=decldadrho/rho
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betas=alpha*beta*(decerfpur*rho/ecerflda-decpur*rho/eclda)
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phis=(rhob*(rhoa/(rhoa + rhob))**(2d0*f13)-rhoa*(rhob/(rhoa + rhob))**(2d0*f13))/(3d0*2d0**f13*rhoa*rhob)
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if (dabs(Ab).le.dabs(beta*tol)) then
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decerfpbedrhoo=decerfldadrho
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else
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Aas=betas/(gamma*Ab)+Aa*(1d0+1d0/Ab)*(decerfpur/phi3-3d0*phis*ecerflda/(rho*phi4))/gamma
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tqs=-2d0*tq*phis/phi
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arglogs=betas*tq*(1d0+Aa*tq)/(Ac*gamma)+beta*tqs*(1d0+Aa*tq)/(Ac*gamma)-beta*tq*Aa*tq*(Aas*tq+Aa*tqs)*(2d0+Aa*tq)/(Ac**2*gamma)
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decerfpbedrhoo=decerfldadrho+gamma*(3d0*rho*phis*phi2*dlog(arglog)+rho*phi3*arglogs/arglog)
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end if
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! derivatives
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vrhoc = vrhoc + decerfpbedrho
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vrhoo = vrhoo + decerfpbedrhoo
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vsigmacc = vsigmacc + decerfpbeddrho2
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end
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subroutine ex_pbe_sr(mu,rho_a,rho_b,grd_rho_a_2,grd_rho_b_2,grd_rho_a_b,ex,vx_rho_a,vx_rho_b,vx_grd_rho_a_2,vx_grd_rho_b_2,vx_grd_rho_a_b)
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BEGIN_DOC
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!mu = range separation parameter
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!
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!rho_a = density alpha
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!
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!rho_b = density beta
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!
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!grd_rho_a_2 = (gradient rho_a)^2
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!
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!grd_rho_b_2 = (gradient rho_b)^2
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!
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!grd_rho_a_b = (gradient rho_a).(gradient rho_b)
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!
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!ex = exchange energy density at the density and corresponding gradients of the density
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!
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!vx_rho_a = d ex / d rho_a
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!
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!vx_rho_b = d ex / d rho_b
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!
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!vx_grd_rho_a_2 = d ex / d grd_rho_a_2
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!
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!vx_grd_rho_b_2 = d ex / d grd_rho_b_2
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!
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!vx_grd_rho_a_b = d ex / d grd_rho_a_b
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END_DOC
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implicit none
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! input
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double precision, intent(in) :: mu,rho_a, rho_b
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double precision, intent(in) :: grd_rho_a_2, grd_rho_b_2, grd_rho_a_b
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! output
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double precision, intent(out) :: ex
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double precision, intent(out) :: vx_rho_a, vx_rho_b
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double precision, intent(out) :: vx_grd_rho_a_2, vx_grd_rho_b_2, vx_grd_rho_a_b
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! function
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double precision berf
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double precision dberfda
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! local
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double precision, parameter :: tol=1d-12
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double precision, parameter :: f13=0.333333333333333d0
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double precision exerflda,vxerflda_a,vxerflda_b
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double precision dexerfldadrho
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double precision exerfpbe_a, exerfpbe_b
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double precision dexerfpbedrho_a, dexerfpbedrho_b
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double precision dexerfpbeddrho2_a, dexerfpbeddrho2_b
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double precision rho,drho2
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double precision rho_a_2, rho_b_2
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double precision t1,t2,t3,t4
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double precision kappa,sq,sqs,sqss,fx,fxs,ksig
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! Parameter of the modified interaction
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! initialization
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ex=0.d0
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vx_rho_a=0.d0
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vx_rho_b=0.d0
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vx_grd_rho_a_2=0.d0
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vx_grd_rho_b_2=0.d0
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vx_grd_rho_a_b=0.d0
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! spin scaling relation Ex[rho_a,rho_b] = (1/2) (Ex[2rho_a,2rho_a] + Ex[2rho_b,2rho_b])
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! two times spin alpha density
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rho = max(rho_a,tol)*2.d0
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! test on density
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if (rho >= tol) then
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! call srlda Ex[2*rho_a,2*rho_a]
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call ex_lda_sr(mu,rho_a,rho_a,exerflda,vxerflda_a,vxerflda_b)
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dexerfldadrho = (vxerflda_a + vxerflda_b)*0.5d0
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! square of two times spin alpha density gradient
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drho2=max(grd_rho_a_2,0d0)*4.0d0
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kappa=0.804d0
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sq=drho2*2.6121172985233599567768d-2*rho**(-8d0/3d0)
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fx=1d0+kappa-kappa/(1d0+berf(1.616204596739954813d-1*mu*rho**(-f13))*sq/kappa)
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exerfpbe_a=exerflda*fx
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! Derivatives
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sqs=-8d0*sq/(3d0*rho)
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fxs=kappa**2*(-1.616204596739954813d-1*mu*rho**(-4d0*f13)/3d0*dberfda(1.616204596739954813d-1*mu*rho**(-f13))*sq+berf(1.616204596739954813d-1*mu*rho**(-f13))*sqs)/(kappa+berf(1.616204596739954813d-1*mu*rho**(-f13))*sq)**2
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dexerfpbedrho_a=dexerfldadrho*fx+exerflda*fxs
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sqss=2.6121172985233599567768d-2*rho**(-8d0/3d0)
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dexerfpbeddrho2_a=exerflda*berf(1.616204596739954813d-1*mu*rho**(-1.d0/3.d0))*sqss*kappa**2/(kappa+berf(1.616204596739954813d-1*mu*rho**(-1.d0/3.d0))*sq)**2
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endif
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! two times spin beta density
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rho = max(rho_b,tol)*2.d0
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! test on density
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if (rho >= tol) then
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! call srlda Ex[2*rho_b,2*rho_b]
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call ex_lda_sr(mu,rho_b,rho_b,exerflda,vxerflda_a,vxerflda_b)
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dexerfldadrho = (vxerflda_a + vxerflda_b)*0.5d0
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! square of two times spin beta density gradient
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drho2=max(grd_rho_b_2,0d0)*4.0d0
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kappa=0.804d0
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sq=drho2*2.6121172985233599567768d-2*rho**(-8d0/3d0)
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fx=1d0+kappa-kappa/(1d0+berf(1.616204596739954813d-1*mu*rho**(-f13))*sq/kappa)
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exerfpbe_b=exerflda*fx
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! Derivatives
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sqs=-8d0*sq/(3d0*rho)
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fxs=kappa**2*(-1.616204596739954813d-1*mu*rho**(-4d0*f13)/3d0*dberfda(1.616204596739954813d-1*mu*rho**(-f13))*sq+berf(1.616204596739954813d-1*mu*rho**(-f13))*sqs)/(kappa+berf(1.616204596739954813d-1*mu*rho**(-f13))*sq)**2
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dexerfpbedrho_b=dexerfldadrho*fx+exerflda*fxs
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sqss=2.6121172985233599567768d-2*rho**(-8d0/3d0)
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dexerfpbeddrho2_b=exerflda*berf(1.616204596739954813d-1*mu*rho**(-1.d0/3.d0))*sqss*kappa**2/(kappa+berf(1.616204596739954813d-1*mu*rho**(-1.d0/3.d0))*sq)**2
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endif
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ex = (exerfpbe_a+exerfpbe_b)*0.5d0
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vx_rho_a = dexerfpbedrho_a
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vx_rho_b = dexerfpbedrho_a
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vx_grd_rho_a_2 = 2.d0*dexerfpbeddrho2_a
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vx_grd_rho_b_2 = 2.d0*dexerfpbeddrho2_b
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vx_grd_rho_a_b = 0.d0
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end
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subroutine ex_pbe_sr_only(mu,rho_a,rho_b,grd_rho_a_2,grd_rho_b_2,grd_rho_a_b,ex)
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BEGIN_DOC
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!rho_a = density alpha
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!
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!rho_b = density beta
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!
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!grd_rho_a_2 = (gradient rho_a)^2
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!
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!grd_rho_b_2 = (gradient rho_b)^2
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!
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!grd_rho_a_b = (gradient rho_a).(gradient rho_b)
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!
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!ex = exchange energy density at point r
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END_DOC
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implicit none
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! input
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double precision, intent(in) :: mu,rho_a, rho_b
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double precision, intent(in) :: grd_rho_a_2, grd_rho_b_2, grd_rho_a_b
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! output
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double precision, intent(out) :: ex
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! function
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double precision berf
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! local
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double precision, parameter :: tol=1d-12
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double precision, parameter :: f13=0.333333333333333d0
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double precision exerflda,vxerflda_a,vxerflda_b
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double precision exerfpbe_a, exerfpbe_b
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double precision rho,drho2
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double precision kappa,sq,fx
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! initialization
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ex=0.d0
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! spin scaling relation Ex[rho_a,rho_b] = (1/2) (Ex[2rho_a,2rho_a] + Ex[2rho_b,2rho_b])
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! two times spin alpha density
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rho = max(rho_a,tol)*2.d0
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! test on density
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if (rho >= tol) then
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! call srlda Ex[2*rho_a,2*rho_a]
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call ex_lda_sr(mu,rho_a,rho_a,exerflda,vxerflda_a,vxerflda_b)
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! square of two times spin alpha density gradient
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drho2=max(grd_rho_a_2,0d0)*4.0d0
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kappa=0.804d0
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sq=drho2*2.6121172985233599567768d-2*rho**(-8d0/3d0)
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fx=1d0+kappa-kappa/(1d0+berf(1.616204596739954813d-1*mu*rho**(-f13))*sq/kappa)
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exerfpbe_a=exerflda*fx
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endif
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! two times spin beta density
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rho = max(rho_b,tol)*2.d0
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! test on density
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if (rho >= tol) then
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! call srlda Ex[2*rho_b,2*rho_b]
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call ex_lda_sr(mu,rho_b,rho_b,exerflda,vxerflda_a,vxerflda_b)
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! square of two times spin beta density gradient
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drho2=max(grd_rho_b_2,0d0)*4.0d0
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kappa=0.804d0
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sq=drho2*2.6121172985233599567768d-2*rho**(-8d0/3d0)
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fx=1d0+kappa-kappa/(1d0+berf(1.616204596739954813d-1*mu*rho**(-f13))*sq/kappa)
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exerfpbe_b=exerflda*fx
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endif
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ex = (exerfpbe_a+exerfpbe_b)*0.5d0
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end
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subroutine ec_pbe_only(mu,rhoc,rhoo,sigmacc,sigmaco,sigmaoo,ec)
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BEGIN_DOC
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! Short-range pbe correlation energy functional for erf interaction
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!
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! input : ==========
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!
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! mu = range separated parameter
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!
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! rhoc, rhoo = total density and spin density
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!
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! sigmacc = square of the gradient of the total density
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!
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! sigmaco = square of the gradient of the spin density
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!
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! sigmaoo = scalar product between the gradient of the total density and the one of the spin density
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!
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! output: ==========
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!
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! ec = correlation energy
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!
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END_DOC
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include 'constants.include.F'
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implicit none
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! input
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double precision, intent(in) :: rhoc,rhoo,mu
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double precision, intent(in) :: sigmacc,sigmaco,sigmaoo
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! output
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double precision, intent(out) :: ec
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! local
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double precision tol
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parameter(tol=1d-12)
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character(len=30) namedummy
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double precision eccerflda
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double precision vrhoccerflda
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double precision vrhoocerflda
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double precision ecclda
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double precision vrhocclda
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double precision vrhooclda
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integer i,igrad
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double precision rho,drho2,rhoa,rhob
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double precision ecerflda
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double precision eclda,decldadrho
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double precision ecerfpbe
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double precision arglog,alpha,beta,gamma
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double precision Aa,Ab,Ac,tq
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double precision zeta,phi,phi2,phi3,phi4
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double precision, parameter :: f13=0.333333333333333d0
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! Parameter of the modified interaction
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ec = 0.d0
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! First-type gradient functional
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igrad=1
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alpha=2.78d0
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gamma=3.1091d-2
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! test on density
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if (dabs(rhoc).lt.tol) return
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double precision :: vc_a,vc_b
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! Spin polarisation
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rhoa=max((rhoc+rhoo)*.5d0,1.0d-15)
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rhob=max((rhoc-rhoo)*.5d0,1.0d-15)
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call ec_lda_sr(mu,rhoa,rhob,eccerflda,vc_a,vc_b)
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ecerflda = eccerflda
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vrhoccerflda = 0.5d0 * (vc_a + vc_b)
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vrhoocerflda = 0.5d0 * (vc_a - vc_b)
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! Density
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rho = rhoc
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rho = max(rho,1.d-10)
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! Square of density gradient
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drho2 = sigmacc
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zeta = (rhoa-rhob)/(rhoa+rhob)
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zeta = max(zeta,1.d-10)
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! lda energy density
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double precision :: vc_a_lda,vc_b_lda
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call ec_lda(rhoa,rhob,ecclda,vc_a_lda,vc_b_lda)
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eclda = ecclda
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decldadrho = 0.5d0 * (vc_a_lda+vc_b_lda)
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decldadrho = 0.5d0 * (vc_a_lda-vc_b_lda)
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if ((ecerflda/eclda).le.0d0) then
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beta=0d0
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else
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beta=6.6725d-2*(ecerflda/eclda)**alpha
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endif
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phi=((1d0+zeta)**(2d0/3d0)+(1d0-zeta)**(2d0/3d0))/2d0
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phi2=phi*phi
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phi3=phi2*phi
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phi4=phi3*phi
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tq=drho2*6.346820607d-2*rho**(-7d0/3d0)/phi2
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Ab=dexp(-ecerflda/(rho*gamma*phi3))-1d0
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if (dabs(Ab).le.dabs(beta*tol)) then
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ecerfpbe=ecerflda
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else
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Aa=beta/(gamma*Ab)
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Ac=1d0+Aa*tq+Aa**2*tq**2
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if (Aa.lt.tol) Aa=tol
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arglog=1d0+beta*(1d0-1d0/Ac)/(gamma*Aa)
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arglog=max(arglog,1.d-10)
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ecerfpbe=ecerflda+rho*phi3*gamma*dlog(arglog)
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end if
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ec = ecerfpbe
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end
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