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https://github.com/pfloos/quack
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remove obselete routines
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@ -1,515 +0,0 @@
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subroutine lsdsr(rs,z,mu,excsr,vxcsrup,vxcsrdown)
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ccc Hartree atomic units used
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ccc for given density parameter 'rs', spin polarization 'z'
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ccc and cutoff parameter 'mu'
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ccc gives the complementary short-range exchange-correlation
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ccc energy (i.e., xc energy of jellium minus xc energy of long-range
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ccc interacting electron gas) => 'excsr'
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ccc and the corresponding exchange-correlation potentials for
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ccc spin-up and spin-down electrons => 'vxcsrup','vxcsrdown'
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ccc from Paziani, Moroni, Gori-Giorgi, and Bachelet, cond-mat/0601353
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implicit none
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double precision rs,z,mu,excsr,vxcsrup,vxcsrdown
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double precision eclr,exlr,ec,ecd,ecz,ex
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double precision vclrup,vclrdown,vxlrup,vxlrdown
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double precision vxup,vxdown,vcup,vcdown
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double precision pi,alpha,cf
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pi=dacos(-1.d0)
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alpha=(4.d0/9.d0/pi)**(1.d0/3.d0)
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cf=1.d0/alpha
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ex=-3.d0*cf/rs/8.d0/pi*((1.d0+z)**(4.d0/3.d0)+
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$ (1.d0-z)**(4.d0/3.d0))
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ex = 0d0
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vxup=-(1.d0+z)**(1.d0/3.d0)*(3.d0/2.d0/pi)**(2.d0/3.d0)/rs
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vxdown=-(1.d0-z)**(1.d0/3.d0)*(3.d0/2.d0/pi)**(2.d0/3.d0)/rs
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vxup = 0d0
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vxdown = 0d0
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call ecPW(rs,z,ec,ecd,ecz)
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vcup=ec-rs/3.d0*ecd-(z-1.d0)*ecz
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vcdown=ec-rs/3.d0*ecd-(z+1.d0)*ecz
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call exchangelr(rs,z,mu,exlr)
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exlr = 0d0
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call vexchangelr(rs,z,mu,vxlrup,vxlrdown)
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vxlrup = 0d0
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vxlrdown = 0d0
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call ecorrlr(rs,z,mu,eclr)
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call vcorrlr(rs,z,mu,vclrup,vclrdown)
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excsr=ex+ec-(exlr+eclr)
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vxcsrup=vxup+vcup-(vxlrup+vclrup)
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vxcsrdown=vxdown+vcdown-(vxlrdown+vclrdown)
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return
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end
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subroutine ecorrlr(rs,z,mu,eclr)
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ccc Hartree atomic units used
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ccc for given density parameter rs, spin polarization z
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ccc and cutoff parameter mu
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ccc gives the correlation energy of the LR gas
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ccc => eclr
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implicit none
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double precision rs,z,mu,eclr,ec,ecd,ecz
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double precision pi,alpha,cf,phi
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double precision g0,dpol,d2anti,d3anti,Qrpa
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double precision coe2,coe3,coe4,coe5
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double precision a1,a2,a3,a4,b0
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double precision q1a,q2a,q3a,t1a,t2a,t3a,adib
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pi=dacos(-1.d0)
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alpha=(4.d0/9.d0/pi)**(1.d0/3.d0)
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cf=1.d0/alpha
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phi=((1.d0+z)**(2.d0/3.d0)+(1.d0-z)**(2.d0/3.d0))/2.d0
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cc parameters from the fit
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adib = 0.784949d0
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q1a = -0.388d0
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q2a = 0.676d0
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q3a = 0.547d0
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t1a = -4.95d0
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t2a = 1.d0
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t3a = 0.31d0
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b0=adib*rs
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d2anti=(q1a*rs+q2a*rs**2)*exp(-abs(q3a)*rs)/rs**2
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d3anti=(t1a*rs+t2a*rs**2)*exp(-abs(t3a)*rs)/rs**3
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coe2=-3.d0/8.d0/rs**3*(1.d0-z**2)*(g0(rs)-0.5d0)
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coe3=-(1.d0-z**2)*g0(rs)/(sqrt(2.d0*pi)*rs**3)
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if(abs(z).eq.1.d0) then
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coe4=-9.d0/64.d0/rs**3*(dpol(rs)
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$ -cf**2*2**(5.d0/3.d0)/5.d0/rs**2)
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coe5=-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*dpol(rs)
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else
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coe4=-9.d0/64.d0/rs**3*(((1.d0+z)/2.d0)**2*
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$ dpol(rs*(2/(1.d0+z))**(1.d0/3.d0))+((1.d0-z)/2.d0)**2
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$ *dpol(rs*(2.d0/(1.d0-z))**(1.d0/3.d0))+
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$ (1.-z**2)*d2anti-cf**2/10.d0*((1.d0+z)**(8.d0/3.d0)
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$ +(1.-z)**(8.d0/3.d0))/rs**2)
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coe5=-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*(((1.d0+z)/2.d0)**2
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$ *dpol(rs*(2.d0/(1.d0+z))**(1.d0/3.d0))+((1.d0-z)/2.d0)**2
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$ *dpol(rs*(2.d0/(1.d0-z))**(1.d0/3.d0))+(1.d0-z**2)*
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$ d3anti)
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endif
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call ecPW(rs,z,ec,ecd,ecz)
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a1=4.d0*b0**6*coe3+b0**8*coe5
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a2=4.d0*b0**6*coe2+b0**8*coe4+6.d0*b0**4*ec
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a3=b0**8*coe3
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a4=b0**6*(b0**2*coe2+4.d0*ec)
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eclr=(phi**3*Qrpa(mu*sqrt(rs)/phi)+a1*mu**3+a2*mu**4+a3*mu**5+
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$ a4*mu**6+b0**8*mu**8*ec)/((1.d0+b0**2*mu**2)**4)
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return
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end
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subroutine vcorrlr(rs,z,mu,vclrup,vclrdown)
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ccc Hartree atomic units used
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ccc for given density parameter rs, spin polarization z
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ccc and cutoff mu it gives the correlation LSD potential for LR interaction
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ccc => vclrup (spin-up electrons), vclrdown (spin-down electrons)
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implicit none
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double precision rs,z,mu,eclr,eclrrs,eclrz,vclrup,vclrdown
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double precision ec,ecd,ecz
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double precision pi,alpha,cf,phi
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double precision g0,dpol,d2anti,d3anti,Qrpa
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double precision g0d,dpold,d2antid,d3antid,Qrpad,x
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double precision coe2,coe3,coe4,coe5
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double precision coe2rs,coe3rs,coe4rs,coe5rs
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double precision coe2z,coe3z,coe4z,coe5z
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double precision a1,a2,a3,a4,a5,b0,a1rs,a2rs,a3rs,a4rs,a5rs,
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$ b0rs,a1z,a2z,a3z,a4z,a5z,b0z
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double precision q1a,q2a,q3a,t1a,t2a,t3a,adib
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pi=dacos(-1.d0)
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alpha=(4.d0/9.d0/pi)**(1.d0/3.d0)
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cf=1.d0/alpha
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phi=((1.d0+z)**(2.d0/3.d0)+(1.d0-z)**(2.d0/3.d0))/2.d0
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cc parameters from the fit
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adib = 0.784949d0
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q1a = -0.388d0
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q2a = 0.676d0
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q3a = 0.547d0
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t1a = -4.95d0
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t2a = 1.d0
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t3a = 0.31d0
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b0=adib*rs
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d2anti=(q1a+q2a*rs)*exp(-q3a*rs)/rs
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d3anti=(t1a+t2a*rs)*exp(-t3a*rs)/rs**2
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d2antid=-((q1a + q1a*q3a*rs + q2a*q3a*rs**2)/
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- rs**2)*exp(-q3a*rs)
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d3antid=-((rs*t2a*(1 + rs*t3a) + t1a*(2 + rs*t3a))/
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- rs**3)*exp(-rs*t3a)
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coe2=-3.d0/8.d0/rs**3*(1.d0-z**2)*(g0(rs)-0.5d0)
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coe2rs=-3.d0/8.d0/rs**3*(1.d0-z**2)*g0d(rs)+
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$ 9.d0/8.d0/rs**4*(1.d0-z**2)*(g0(rs)-0.5d0)
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coe2z=-3.d0/8.d0/rs**3*(-2.d0*z)*(g0(rs)-0.5d0)
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coe3=-(1.d0-z**2)*g0(rs)/(sqrt(2.d0*pi)*rs**3)
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coe3rs=-(1.d0-z**2)*g0d(rs)/(sqrt(2.d0*pi)*rs**3)+
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$ 3.d0*(1.d0-z**2)*g0(rs)/(sqrt(2.d0*pi)*rs**4)
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coe3z=2.d0*z*g0(rs)/(sqrt(2.d0*pi)*rs**3)
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if(abs(z).eq.1.d0) then
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coe4=-9.d0/64.d0/rs**3*(dpol(rs)
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$ -cf**2*2**(5.d0/3.d0)/5.d0/rs**2)
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coe4rs=-3.d0/rs*coe4-9.d0/64.d0/rs**3*(dpold(rs)
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$ +2.d0*cf**2*2**(5.d0/3.d0)/5.d0/rs**3)
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coe4z=-9.d0/64.d0/rs**3*(dpol(rs)-rs/6.d0*dpold(rs)-2.d0*d2anti
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$ -4.d0/15.d0/rs**2*cf**2*2.d0**(5.d0/3.d0))*z
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coe5=-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*dpol(rs)
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coe5rs=-3.d0/rs*coe5-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*dpold(rs)
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coe5z=-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*(dpol(rs)-rs/6.d0*
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$ dpold(rs)-2.d0*d3anti)*z
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else
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coe4=-9.d0/64.d0/rs**3*(((1.d0+z)/2.d0)**2*
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$ dpol(rs*(2/(1.d0+z))**(1.d0/3.d0))+((1.d0-z)/2.d0)**2
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$ *dpol(rs*(2.d0/(1.d0-z))**(1.d0/3.d0))+
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$ (1.-z**2)*d2anti-cf**2/10.d0*((1.d0+z)**(8.d0/3.d0)
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$ +(1.-z)**(8.d0/3.d0))/rs**2)
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coe4rs=-3.d0/rs*coe4-9.d0/64.d0/rs**3*(
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$ ((1.d0+z)/2.d0)**(5.d0/3.d0)*dpold(rs*(2/(1.d0+z))**
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$ (1.d0/3.d0))+((1.d0-z)/2.d0)**(5.d0/3.d0)*
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$ dpold(rs*(2/(1.d0-z))**(1.d0/3.d0))+(1.d0-z**2)*
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$ d2antid+cf**2/5.d0*((1.d0+z)**(8.d0/3.d0)
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$ +(1.d0-z)**(8.d0/3.d0))/rs**3)
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coe4z=-9.d0/64.d0/rs**3*(1.d0/2.d0*(1.d0+z)*
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$ dpol(rs*(2/(1.d0+z))**(1.d0/3.d0))-1.d0/2.d0*(1.d0-z)*
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$ dpol(rs*(2/(1.d0-z))**(1.d0/3.d0))-rs/6.d0*
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$ ((1.d0+z)/2.d0)**(2.d0/3.d0)*dpold(rs*(2/(1.d0+z))
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$ **(1.d0/3.d0))+rs/6.d0*((1.d0-z)/2.d0)**(2.d0/3.d0)
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$ *dpold(rs*(2/(1.d0-z))**(1.d0/3.d0))-2.d0*z*d2anti-
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$ 4.d0/15.d0/rs**2*cf**2*((1.d0+z)**(5.d0/3.d0)-
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$ (1.d0-z)**(5.d0/3.d0)))
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coe5=-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*(((1.d0+z)/2.d0)**2
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$ *dpol(rs*(2.d0/(1.d0+z))**(1.d0/3.d0))+((1.d0-z)/2.d0)**2
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$ *dpol(rs*(2.d0/(1.d0-z))**(1.d0/3.d0))+(1.d0-z**2)*
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$ d3anti)
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coe5rs=-3.d0/rs*coe5-9.d0/(40.d0*sqrt(2.d0*pi)*rs**3)*(
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$ ((1.d0+z)/2.d0)**(5.d0/3.d0)*dpold(rs*(2/(1.d0+z))**
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$ (1.d0/3.d0))+((1.d0-z)/2.d0)**(5.d0/3.d0)*
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$ dpold(rs*(2/(1.d0-z))**(1.d0/3.d0))+(1.d0-z**2)*
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$ d3antid)
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coe5z=-9.d0/40.d0/(sqrt(2.d0*pi)*rs**3)*(1.d0/2.d0*(1.d0+z)*
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$ dpol(rs*(2/(1.d0+z))**(1.d0/3.d0))-1.d0/2.d0*(1.d0-z)*
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$ dpol(rs*(2/(1.d0-z))**(1.d0/3.d0))-rs/6.d0*
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$ ((1.d0+z)/2.d0)**(2.d0/3.d0)*dpold(rs*(2/(1.d0+z))
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$ **(1.d0/3.d0))+rs/6.d0*((1.d0-z)/2.d0)**(2.d0/3.d0)
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$ *dpold(rs*(2/(1.d0-z))**(1.d0/3.d0))-2.d0*z*d3anti)
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endif
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call ecPW(rs,z,ec,ecd,ecz)
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a1=4.d0*b0**6*coe3+b0**8*coe5
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a1rs=24.d0*adib*b0**5*coe3+4.d0*b0**6*coe3rs+8.d0*adib*b0**7*
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$ coe5+b0**8*coe5rs
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a1z=4.d0*b0**6*coe3z+b0**8*coe5z
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a2=4.d0*b0**6*coe2+b0**8*coe4+6.d0*b0**4*ec
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a2rs=24.d0*adib*b0**5*coe2+4.d0*b0**6*coe2rs+8.d0*adib*b0**7*
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$ coe4+b0**8*coe4rs+24.d0*adib*b0**3*ec+6.d0*b0**4*ecd
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a2z=4.d0*b0**6*coe2z+b0**8*coe4z+6.d0*b0**4*ecz
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a3=b0**8*coe3
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a3rs=8.d0*adib*b0**7*coe3+b0**8*coe3rs
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a3z=b0**8*coe3z
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a4=b0**6*(b0**2*coe2+4.d0*ec)
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a4rs=8.d0*adib*b0**7*coe2+b0**8*coe2rs+24.d0*adib*b0**5*ec+
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$ 4.d0*b0**6*ecd
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a4z=b0**6*(b0**2*coe2z+4.d0*ecz)
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a5=b0**8*ec
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a5rs=8.d0*adib*b0**7*ec+b0**8*ecd
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a5z=b0**8*ecz
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x=mu*sqrt(rs)/phi
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eclr=(phi**3*Qrpa(x)+a1*mu**3+a2*mu**4+a3*mu**5+
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$ a4*mu**6+a5*mu**8)/((1.d0+b0**2*mu**2)**4)
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eclrrs=-4.d0/(1.d0+b0**2*mu**2)*2.d0*adib*b0*mu**2*eclr+
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$ 1.d0/((1.d0+b0**2*mu**2)**4)*(phi**2*mu/(2.d0*sqrt(rs))
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$ *Qrpad(x)+
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$ a1rs*mu**3+a2rs*mu**4+a3rs*mu**5+a4rs*mu**6+a5rs*mu**8)
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if(z.eq.1.d0) then
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vclrup=eclr-rs/3.d0*eclrrs
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vclrdown=0.d0
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elseif(z.eq.-1.d0) then
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vclrup=0.d0
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vclrdown=eclr-rs/3.d0*eclrrs
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else
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eclrz=(phi**2*((1.d0+z)**(-1.d0/3.d0)-(1.d0-z)**(-1.d0/3.d0))
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$ *Qrpa(x)-phi*Qrpad(x)*mu*sqrt(rs)*((1.d0+z)**(-1.d0/3.d0)
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$ -(1.d0-z)**(-1.d0/3.d0))/3.d0+
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$ a1z*mu**3+a2z*mu**4+a3z*mu**5+
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$ a4z*mu**6+a5z*mu**8)/((1.d0+b0**2*mu**2)**4)
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vclrup=eclr-rs/3.d0*eclrrs-(z-1.d0)*eclrz
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vclrdown=eclr-rs/3.d0*eclrrs-(z+1.d0)*eclrz
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endif
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return
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end
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double precision function g0(x)
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ccc on-top pair-distribution function
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ccc Gori-Giorgi and Perdew, PRB 64, 155102 (2001)
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ccc x -> rs
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implicit none
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double precision C0f,D0f,E0f,F0f,x
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C0f = 0.0819306d0
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D0f = 0.752411d0
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E0f = -0.0127713d0
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F0f = 0.00185898d0
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g0=(1.d0-(0.7317d0-D0f)*x+C0f*x**2+E0f*x**3+
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$ F0f*x**4)*exp(-abs(D0f)*x)/2.d0
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return
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end
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double precision function g0d(rs)
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ccc derivative of on-top pair-distribution function
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ccc Gori-Giorgi and Perdew, PRB 64, 155102 (2001)
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implicit none
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double precision Bg0,Cg0,Dg0,Eg0,Fg0,rs
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Cg0 = 0.0819306d0
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Fg0 = 0.752411d0
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Dg0 = -0.0127713d0
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Eg0 = 0.00185898d0
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Bg0 =0.7317d0-Fg0
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g0d=(-Bg0+2*Cg0*rs+3*Dg0*rs**2+4*Eg0*rs**3)/2.d0*exp(-Fg0*rs)
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- - (Fg0*(1 - Bg0*rs + Cg0*rs**2 + Dg0*rs**3 + Eg0*rs**4))/
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- 2.d0*exp(-Fg0*rs)
|
||||
return
|
||||
end
|
||||
|
||||
|
||||
double precision function dpol(rs)
|
||||
implicit none
|
||||
double precision cf,pi,rs,p2p,p3p
|
||||
pi=dacos(-1.d0)
|
||||
cf=(9.d0*pi/4.d0)**(1.d0/3.d0)
|
||||
p2p = 0.04d0
|
||||
p3p = 0.4319d0
|
||||
dpol=2.d0**(5.d0/3.d0)/5.d0*cf**2/rs**2*(1.d0+(p3p-0.454555d0)*rs)
|
||||
$ /(1.d0+p3p*rs+p2p*rs**2)
|
||||
return
|
||||
end
|
||||
|
||||
double precision function dpold(rs)
|
||||
implicit none
|
||||
double precision cf,pi,rs,p2p,p3p
|
||||
pi=dacos(-1.d0)
|
||||
cf=(9.d0*pi/4.d0)**(1.d0/3.d0)
|
||||
p2p = 0.04d0
|
||||
p3p = 0.4319d0
|
||||
dpold=2.d0**(5.d0/3.d0)/5.d0*cf**2*
|
||||
- (-2. + (0.454555 - 4.*p3p)*rs +
|
||||
- (-4.*p2p +
|
||||
- (0.90911 - 2.*p3p)*p3p)*rs**2
|
||||
- + p2p*(1.363665 - 3.*p3p)*
|
||||
- rs**3)/
|
||||
- (rs**3*(1. + p3p*rs + p2p*rs**2)**2)
|
||||
return
|
||||
end
|
||||
|
||||
double precision function Qrpa(x)
|
||||
implicit none
|
||||
double precision pi,a2,b2,c2,d2,x,Acoul
|
||||
pi=dacos(-1.d0)
|
||||
Acoul=2.d0*(log(2.d0)-1.d0)/pi**2
|
||||
a2 = 5.84605d0
|
||||
c2 = 3.91744d0
|
||||
d2 = 3.44851d0
|
||||
b2=d2-3.d0/(2.d0*pi*Acoul)*(4.d0/(9.d0*pi))**(1.d0/3.d0)
|
||||
Qrpa=Acoul*log((1.d0+a2*x+b2*x**2+c2*x**3)/(1.d0+a2*x+d2*x**2))
|
||||
return
|
||||
end
|
||||
|
||||
double precision function Qrpad(x)
|
||||
implicit none
|
||||
double precision pi,a2,b2,c2,d2,x,Acoul
|
||||
pi=dacos(-1.d0)
|
||||
Acoul=2.d0*(log(2.d0)-1.d0)/pi**2
|
||||
a2 = 5.84605d0
|
||||
c2 = 3.91744d0
|
||||
d2 = 3.44851d0
|
||||
b2=d2-3.d0/(2.d0*pi*Acoul)*(4.d0/(9.d0*pi))**(1.d0/3.d0)
|
||||
Qrpad=Acoul*((x*(b2*(2.d0 + a2*x) +
|
||||
- c2*x*(3.d0 + 2.d0*a2*x) +
|
||||
- d2*(-2.d0 - a2*x + c2*x**3)))/
|
||||
- ((1.d0 + a2*x + d2*x**2)*
|
||||
- (1.d0 + a2*x + b2*x**2 + c2*x**3)))
|
||||
return
|
||||
end
|
||||
|
||||
subroutine exchangelr(rs,z,mu,exlr)
|
||||
ccc Hartree atomic units used
|
||||
ccc for given density parameter rs, spin polarization z
|
||||
ccc and cutoff mu it gives the exchange energy of the LR gas
|
||||
ccc => exlr
|
||||
implicit none
|
||||
double precision rs,z,mu,exlr
|
||||
double precision pi,alpha,fx,y
|
||||
pi=dacos(-1.d0)
|
||||
alpha=(4.d0/9.d0/pi)**(1.d0/3.d0)
|
||||
if(abs(z).eq.1.d0) then
|
||||
y=mu*alpha*rs/2.d0/2.d0**(1.d0/3.d0)
|
||||
fx=-((-3*y + 4*y**3 +(2*y - 4*y**3)*exp(-1./(4.*y**2)) +
|
||||
$ sqrt(pi)*erf(1/(2.*y)))/pi)
|
||||
exlr=mu*fx
|
||||
else
|
||||
y=mu*alpha*rs/2.d0/(1.+z)**(1.d0/3.d0)
|
||||
fx=-((-3*y + 4*y**3 +(2*y - 4*y**3)*exp(-1./(4.*y**2)) +
|
||||
$ sqrt(pi)*erf(1/(2.*y)))/pi)
|
||||
exlr=(1.d0+z)*mu*fx/2.d0
|
||||
y=mu*alpha*rs/2.d0/(1.-z)**(1.d0/3.d0)
|
||||
fx=-((-3*y + 4*y**3 +(2*y - 4*y**3)*exp(-1./(4.*y**2)) +
|
||||
$ sqrt(pi)*erf(1/(2.*y)))/pi)
|
||||
exlr=exlr+(1.d0-z)*mu*fx/2.d0
|
||||
endif
|
||||
return
|
||||
end
|
||||
|
||||
subroutine vexchangelr(rs,z,mu,vxlrup,vxlrdown)
|
||||
ccc Hartree atomic units used
|
||||
ccc for given density parameter rs, spin polarization z
|
||||
ccc and cutoff mu it gives the exchange LSD potential for LR interaction
|
||||
ccc => vxlrup (spin-up electrons), vxlrdown (spin-down electrons)
|
||||
implicit none
|
||||
double precision rs,z,mu,vxlrup,vxlrdown
|
||||
double precision pi,alpha,fx,fx1,y,exlr,derrs,derz
|
||||
pi=dacos(-1.d0)
|
||||
alpha=(4.d0/9.d0/pi)**(1.d0/3.d0)
|
||||
if(z.eq.1.d0) then
|
||||
vxlrup=(rs*alpha*mu**2)/
|
||||
- (2**(1.d0/3.d0)*pi) - (rs*alpha*mu**2)/(2**(1.d0/3.d0)*pi)*
|
||||
- exp(-2**(2.d0/3.d0)/(rs**2*alpha**2*mu**2)) -
|
||||
- (mu*erf(2**(1.d0/3.d0)/(rs*alpha*mu)))/sqrt(Pi)
|
||||
vxlrdown=0.d0
|
||||
elseif(z.eq.-1.d0) then
|
||||
vxlrdown=(rs*alpha*mu**2)/
|
||||
- (2**(1.d0/3.d0)*pi) - (rs*alpha*mu**2)/(2**(1.d0/3.d0)*pi)*
|
||||
- exp(-2**(2.d0/3.d0)/(rs**2*alpha**2*mu**2)) -
|
||||
- (mu*erf(2**(1.d0/3.d0)/(rs*alpha*mu)))/sqrt(Pi)
|
||||
vxlrup=0.d0
|
||||
else
|
||||
y=mu*alpha*rs/2.d0/(1.+z)**(1.d0/3.d0)
|
||||
fx=-((-3*y + 4*y**3 +(2*y - 4*y**3)*exp(-1./(4.*y**2)) +
|
||||
$ sqrt(pi)*erf(1/(2.*y)))/pi)
|
||||
fx1=(3.d0*(1 + (-4.d0 + 4.d0*exp(-1.d0/(4.d0*y**2)))*y**2))/pi
|
||||
derrs=1.d0/4.d0*(1.d0+z)**(2.d0/3.d0)*mu**2*alpha*fx1
|
||||
derz=1.d0/2.d0*mu*fx-1.d0/6.d0*fx1*mu*y
|
||||
vxlrup=rs/3.d0*derrs+(z-1.d0)*derz
|
||||
vxlrdown=rs/3.d0*derrs+(z+1.d0)*derz
|
||||
|
||||
y=mu*alpha*rs/2.d0/(1.-z)**(1.d0/3.d0)
|
||||
fx=-((-3*y + 4*y**3 +(2*y - 4*y**3)*exp(-1./(4.*y**2)) +
|
||||
$ sqrt(pi)*erf(1/(2.*y)))/pi)
|
||||
fx1=(3.d0*(1 + (-4.d0 + 4.d0*exp(-1.d0/(4.d0*y**2)))*y**2))/pi
|
||||
derrs=1.d0/4.d0*(1.d0-z)**(2.d0/3.d0)*mu**2*alpha*fx1
|
||||
derz=-1.d0/2.d0*mu*fx+1.d0/6.d0*fx1*mu*y
|
||||
vxlrup=vxlrup+rs/3.d0*derrs+(z-1.d0)*derz
|
||||
vxlrdown=vxlrdown+rs/3.d0*derrs+(z+1.d0)*derz
|
||||
|
||||
call exchangelr(rs,z,mu,exlr)
|
||||
vxlrup=exlr-vxlrup
|
||||
vxlrdown=exlr-vxlrdown
|
||||
endif
|
||||
return
|
||||
end
|
||||
|
||||
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
|
||||
c correlation energy and its derivative w.r.t. rs and z at mu=infinity
|
||||
c Perdew & Wang PRB 45, 13244 (1992)
|
||||
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
|
||||
subroutine ecPW(x,y,ec,ecd,ecz)
|
||||
c in Hartree; ec=ec(rs,zeta)
|
||||
c x -> rs; y -> zeta
|
||||
ccc ecd is d/drs ec
|
||||
ccc ecz is d/dz ec
|
||||
implicit none
|
||||
double precision pi,f02,ff,x,y,ec,ecd,ec0,ec0d,ec1,ec1d,
|
||||
$ aaa,G,Gd,alfac,alfacd,ecz
|
||||
pi=dacos(-1.d0)
|
||||
|
||||
f02=4.d0/(9.d0*(2.d0**(1.d0/3.d0)-1.d0))
|
||||
|
||||
ff=((1.d0+y)**(4.d0/3.d0)+(1.d0-y)**(4.d0/3.d0)-
|
||||
$ 2.d0)/(2.d0**(4.d0/3.d0)-2.d0)
|
||||
|
||||
aaa=(1.d0-log(2.d0))/pi**2
|
||||
call GPW(x,aaa,0.21370d0,7.5957d0,3.5876d0,
|
||||
$ 1.6382d0,0.49294d0,G,Gd)
|
||||
ec0=G
|
||||
ec0d=Gd
|
||||
|
||||
aaa=aaa/2.d0
|
||||
call GPW(x,aaa,0.20548d0,14.1189d0,6.1977d0,
|
||||
$ 3.3662d0,0.62517d0,G,Gd)
|
||||
ec1=G
|
||||
ec1d=Gd
|
||||
call GPW(x,0.016887d0,0.11125d0,10.357d0,3.6231d0,
|
||||
$ 0.88026d0,0.49671d0,G,Gd)
|
||||
alfac=-G
|
||||
alfacd=-Gd
|
||||
|
||||
ec=ec0+alfac*ff/f02*(1.d0-y**4)+(ec1-ec0)*ff*y**4
|
||||
ecd=ec0d+alfacd*ff/f02*(1.d0-y**4)+(ec1d-ec0d)*
|
||||
$ ff*y**4
|
||||
ecz=alfac*(-4.d0*y**3)*ff/f02+alfac*(1.d0-y**4)/f02*
|
||||
$ 4.d0/3.d0*((1.d0+y)**(1.d0/3.d0)-(1.d0-y)**(1.d0/3.d0))/
|
||||
$ (2.d0**(4.d0/3.d0)-2.d0)+(ec1-ec0)*(4.d0*y**3*ff+
|
||||
$ 4.d0/3.d0*((1.d0+y)**(1.d0/3.d0)-(1.d0-y)**(1.d0/3.d0))/
|
||||
$ (2.d0**(4.d0/3.d0)-2.d0)*y**4)
|
||||
|
||||
return
|
||||
end
|
||||
|
||||
subroutine GPW(x,Ac,alfa1,beta1,beta2,beta3,beta4,G,Gd)
|
||||
ccc Gd is d/drs G
|
||||
implicit none
|
||||
double precision G,Gd,Ac,alfa1,beta1,beta2,beta3,beta4,x
|
||||
G=-2.d0*Ac*(1.d0+alfa1*x)*dlog(1.d0+1.d0/(2.d0*
|
||||
$ Ac*(beta1*x**0.5d0+
|
||||
$ beta2*x+beta3*x**1.5d0+beta4*x**2)))
|
||||
Gd=(1.d0+alfa1*x)*(beta2+beta1/(2.d0*sqrt(x))+3.d0*beta3*
|
||||
$ sqrt(x)/2.d0+2.d0*beta4*x)/((beta1*sqrt(x)+beta2*x+
|
||||
$ beta3*x**(3.d0/2.d0)+beta4*x**2)**2*(1.d0+1.d0/
|
||||
$ (2.d0*Ac*(beta1*sqrt(x)+beta2*x+beta3*x**(3.d0/2.d0)+
|
||||
$ beta4*x**2))))-2.d0*Ac*alfa1*dlog(1.d0+1.d0/(2.d0*Ac*
|
||||
$ (beta1*sqrt(x)+beta2*x+beta3*x**(3.d0/2.d0)+
|
||||
$ beta4*x**2)))
|
||||
return
|
||||
end
|
||||
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
|
||||
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
|
||||
@ -1,10 +0,0 @@
|
||||
default:
|
||||
ninja
|
||||
make -C ..
|
||||
|
||||
clean:
|
||||
ninja -t clean
|
||||
|
||||
debug:
|
||||
ninja -t clean
|
||||
make -C .. debug
|
||||
@ -1,90 +0,0 @@
|
||||
subroutine basis_correction(nBas,nO,nShell,CenterShell,TotAngMomShell,KShell,DShell,ExpShell, &
|
||||
ERI,e,c,P,eG0W0)
|
||||
|
||||
! Compute the basis set incompleteness error
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas
|
||||
integer,intent(in) :: nO
|
||||
|
||||
integer,intent(in) :: nShell
|
||||
integer,intent(in) :: TotAngMomShell(maxShell),KShell(maxShell)
|
||||
double precision,intent(in) :: CenterShell(maxShell,ncart),DShell(maxShell,maxK),ExpShell(maxShell,maxK)
|
||||
|
||||
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
|
||||
double precision,intent(in) :: e(nBas)
|
||||
double precision,intent(in) :: c(nBas,nBas)
|
||||
double precision,intent(in) :: P(nBas,nBas)
|
||||
|
||||
double precision,intent(in) :: eG0W0(nBas)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: SGn
|
||||
integer :: nRad
|
||||
integer :: nAng
|
||||
integer :: nGrid
|
||||
double precision,allocatable :: root(:,:)
|
||||
double precision,allocatable :: weight(:)
|
||||
double precision,allocatable :: AO(:,:)
|
||||
double precision,allocatable :: dAO(:,:,:)
|
||||
double precision,allocatable :: MO(:,:)
|
||||
double precision,allocatable :: dMO(:,:,:)
|
||||
double precision,allocatable :: rho(:)
|
||||
double precision,allocatable :: f(:)
|
||||
double precision,allocatable :: mu(:)
|
||||
|
||||
! Output variables
|
||||
|
||||
! Hello world
|
||||
|
||||
write(*,*)
|
||||
write(*,*)'************************************************'
|
||||
write(*,*)'| Basis set incompleteness correction |'
|
||||
write(*,*)'************************************************'
|
||||
write(*,*)
|
||||
|
||||
! Set quadrature grid
|
||||
|
||||
SGn = 1
|
||||
|
||||
call read_grid(SGn,nRad,nAng,nGrid)
|
||||
|
||||
! Memory allocation
|
||||
|
||||
allocate(root(ncart,nGrid),weight(nGrid))
|
||||
allocate(AO(nBas,nGrid),dAO(ncart,nBas,nGrid),MO(nBas,nGrid),dMO(ncart,nBas,nGrid))
|
||||
allocate(rho(nGrid),f(nGrid),mu(nGrid))
|
||||
|
||||
call quadrature_grid(nRad,nAng,nGrid,root,weight)
|
||||
|
||||
! Calculate AO values at grid points
|
||||
|
||||
call AO_values_grid(nBas,nShell,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,nGrid,root,AO,dAO)
|
||||
|
||||
! Calculate MO values at grid points
|
||||
|
||||
call MO_values_grid(nBas,nGrid,c,AO,dAO,MO,dMO)
|
||||
|
||||
! Compute one-electron density at grid points
|
||||
|
||||
call density(nGrid,nBas,P,AO,rho)
|
||||
|
||||
! Compute range-sepration function
|
||||
|
||||
call f_grid(nBas,nO,nGrid,MO,ERI,f)
|
||||
call mu_grid(nGrid,rho,f,mu)
|
||||
|
||||
! Compute energy correction
|
||||
|
||||
call ec_srlda(nGrid,weight,rho,mu)
|
||||
|
||||
! Compute orbital corrections
|
||||
|
||||
call fc_srlda(nBas,nGrid,weight,MO,rho,mu,eG0W0)
|
||||
|
||||
end subroutine basis_correction
|
||||
File diff suppressed because it is too large
Load Diff
@ -1,52 +0,0 @@
|
||||
subroutine ec_srlda(nGrid,weight,rho,mu)
|
||||
|
||||
! Compute sr-lda ec
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nGrid
|
||||
double precision,intent(in) :: weight(nGrid)
|
||||
double precision,intent(in) :: rho(nGrid)
|
||||
double precision,intent(in) :: mu(nGrid)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: iG
|
||||
double precision :: r,ra,rb
|
||||
double precision :: rs
|
||||
double precision :: ec_lda,ecmd_lda
|
||||
double precision :: ec,ecmd,vcup,vcdw
|
||||
|
||||
! Initialization
|
||||
|
||||
ec_lda = 0d0
|
||||
ecmd_lda = 0d0
|
||||
|
||||
do iG=1,ngrid
|
||||
|
||||
r = max(0d0,rho(iG))
|
||||
ra = 0.5d0*r
|
||||
rb = 0.5d0*r
|
||||
|
||||
if(r > threshold) then
|
||||
|
||||
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
|
||||
|
||||
call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
|
||||
call ESRC_MD_LDAERF(mu(iG),ra,rb,.true.,ecmd)
|
||||
ec_lda = ec_lda + weight(iG)*ec*r
|
||||
ecmd_lda = ecmd_lda + weight(iG)*ecmd*r
|
||||
|
||||
end if
|
||||
|
||||
end do
|
||||
|
||||
write(*,*)
|
||||
write(*,'(A32,1X,F16.10)') 'Ec(sr-LDA) = ',ec_lda
|
||||
write(*,'(A32,1X,F16.10)') 'Ecmd(sr-LDA) = ',ec_lda + ecmd_lda
|
||||
write(*,*)
|
||||
|
||||
end subroutine ec_srlda
|
||||
@ -1,200 +0,0 @@
|
||||
!****************************************************************************
|
||||
subroutine ESRC_MD_LDAERF (mu,rho_a,rho_b,dospin,e)
|
||||
!*****************************************************************************
|
||||
! Short-range spin-dependent LDA correlation functional with multideterminant reference
|
||||
! for OEP calculations from Section V of
|
||||
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
|
||||
!
|
||||
! Input: rhot : total density
|
||||
! rhos : spin density
|
||||
! mu : Interation parameter
|
||||
! dospin : use spin density
|
||||
!
|
||||
! Ouput: e : energy
|
||||
!
|
||||
! Created: 26-08-11, J. Toulouse
|
||||
!*****************************************************************************
|
||||
implicit none
|
||||
|
||||
double precision, intent(in) :: rho_a,rho_b,mu
|
||||
logical, intent(in) :: dospin
|
||||
double precision, intent(out):: e
|
||||
|
||||
double precision :: e1
|
||||
double precision :: rhoa,rhob
|
||||
double precision :: rhot, rhos
|
||||
rhoa=max(rho_a,1.0d-15)
|
||||
rhob=max(rho_b,1.0d-15)
|
||||
rhot = rhoa + rhob
|
||||
rhos = rhoa - rhob
|
||||
|
||||
call ec_only_lda_sr(mu,rho_a,rho_b,e1)
|
||||
if(isnan(e1))then
|
||||
print*,'e1 is NaN'
|
||||
print*,mu,rho_a,rho_b
|
||||
stop
|
||||
endif
|
||||
e1 = 0d0
|
||||
call DELTA_LRSR_LDAERF (rhot,rhos,mu,dospin,e)
|
||||
if(isnan(e))then
|
||||
print*,'e is NaN'
|
||||
print*,mu,rhot,rhos
|
||||
stop
|
||||
endif
|
||||
e = e1 + e
|
||||
|
||||
end
|
||||
|
||||
!****************************************************************************
|
||||
subroutine DELTA_LRSR_LDAERF (rhot,rhos,mu,dospin,e)
|
||||
!*****************************************************************************
|
||||
! LDA approximation to term Delta_(LR-SR) from Eq. 42 of
|
||||
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
|
||||
!
|
||||
! Input: rhot : total density
|
||||
! rhos : spin density
|
||||
! mu : Interation parameter
|
||||
! dospin : use spin density
|
||||
!
|
||||
! Ouput: e : energy
|
||||
!
|
||||
! Warning: not tested for z != 0
|
||||
!
|
||||
! Created: 26-08-11, J. Toulouse
|
||||
!*****************************************************************************
|
||||
implicit none
|
||||
|
||||
double precision rhot, rhos, mu
|
||||
logical dospin
|
||||
double precision e
|
||||
|
||||
double precision f13, f83, pi, rsfac, alpha2
|
||||
double precision rs, rs2, rs3
|
||||
|
||||
double precision rhoa, rhob, z, z2, onepz, onemz, zp, zm, phi8
|
||||
double precision g0s,g0f
|
||||
double precision bd2, bd3
|
||||
double precision c45, c4, c5
|
||||
double precision bc2, bc4, bc3t, bc5t, d0
|
||||
double precision delta2,delta3,delta4,delta5,delta6
|
||||
double precision delta
|
||||
|
||||
parameter(f13 = 0.333333333333333d0)
|
||||
parameter(f83 = 2.6666666666666665d0)
|
||||
parameter(pi = 3.141592653589793d0)
|
||||
parameter(rsfac = 0.620350490899400d0)
|
||||
parameter(alpha2 = 0.2715053589826032d0)
|
||||
|
||||
rs = rsfac/(rhot**f13)
|
||||
rs2 = rs*rs
|
||||
rs3 = rs2*rs
|
||||
|
||||
! Spin-unpolarized case
|
||||
if (.not.dospin) then
|
||||
z = 0.d0
|
||||
|
||||
! Spin-polarized case
|
||||
else
|
||||
rhoa=max((rhot+rhos)*.5d0,1.0d-15)
|
||||
rhob=max((rhot-rhos)*.5d0,1.0d-15)
|
||||
z=min((rhoa-rhob)/(rhoa+rhob),0.9999999999d0)
|
||||
endif
|
||||
|
||||
z2=z*z
|
||||
|
||||
bd2=dexp(-0.547d0*rs)*(-0.388d0*rs+0.676*rs2)/rs2
|
||||
bd3=dexp(-0.31d0*rs)*(-4.95d0*rs+rs2)/rs3
|
||||
|
||||
onepz=1.d0+z
|
||||
onemz=1.d0-z
|
||||
phi8=0.5d0*(onepz**f83+onemz**f83)
|
||||
|
||||
zp=onepz/2.d0
|
||||
zm=onemz/2.d0
|
||||
c45=(zp**2)*g0s(rs*zp**(-f13))+(zm**2)*g0s(rs*zm**(-f13))
|
||||
c4=c45+(1.d0-z2)*bd2-phi8/(5.d0*alpha2*rs2)
|
||||
c5=c45+(1.d0-z2)*bd3
|
||||
|
||||
bc2=-3.d0*(1-z2)*(g0f(rs)-0.5d0)/(8.d0*rs3)
|
||||
bc4=-9.d0*c4/(64.d0*rs3)
|
||||
bc3t=-(1-z2)*g0f(rs)*(2.d0*dsqrt(2.d0)-1)/(2.d0*dsqrt(pi)*rs3)
|
||||
bc5t = -3.d0*c5*(3.d0-dsqrt(2.d0))/(20.d0*dsqrt(2.d0*pi)*rs3)
|
||||
|
||||
d0=(0.70605d0+0.12927d0*z2)*rs
|
||||
delta2=0.073867d0*(rs**(1.5d0))
|
||||
delta3=4*(d0**6)*bc3t+(d0**8)*bc5t;
|
||||
delta4=4*(d0**6)*bc2+(d0**8)*bc4;
|
||||
delta5=(d0**8)*bc3t;
|
||||
delta6=(d0**8)*bc2;
|
||||
delta=(delta2*(mu**2)+delta3*(mu**3)+delta4*(mu**4)+delta5*(mu**5)+delta6*(mu**6))/((1+(d0**2)*(mu**2))**4)
|
||||
|
||||
|
||||
! multiply by rhot to get energy density
|
||||
! e=delta*rhot
|
||||
e=delta
|
||||
|
||||
end
|
||||
|
||||
!*****************************************************************************
|
||||
double precision function g0s(rs)
|
||||
!*****************************************************************************
|
||||
! g"(0,rs,z=1) from Eq. 32 of
|
||||
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
|
||||
!
|
||||
! Created: 26-08-11, J. Toulouse
|
||||
!*****************************************************************************
|
||||
implicit none
|
||||
double precision rs
|
||||
double precision rs2, f53, alpha2
|
||||
parameter(f53 = 1.6666666666666667d0)
|
||||
parameter(alpha2 = 0.2715053589826032d0)
|
||||
rs2=rs*rs
|
||||
g0s=(2.d0**f53)*(1.d0-0.02267d0*rs)/((5.d0*alpha2*rs2)*(1.d0+0.4319d0*rs+0.04d0*rs2))
|
||||
end
|
||||
|
||||
double precision function g0f(x)
|
||||
!cc on-top pair-distribution function
|
||||
!cc Gori-Giorgi and Perdew, PRB 64, 155102 (2001)
|
||||
!cc x -> rs
|
||||
implicit none
|
||||
double precision C0f,D0f,E0f,F0f,x
|
||||
C0f = 0.0819306d0
|
||||
D0f = 0.752411d0
|
||||
E0f = -0.0127713d0
|
||||
F0f = 0.00185898d0
|
||||
g0f=(1.d0-(0.7317d0-D0f)*x+C0f*x**2+E0f*x**3+ &
|
||||
F0f*x**4)*exp(-abs(D0f)*x)/2.d0
|
||||
return
|
||||
end
|
||||
|
||||
subroutine ec_only_lda_sr(mu,rho_a,rho_b,ec)
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
double precision, intent(out) :: ec
|
||||
double precision, intent(in) :: mu,rho_a,rho_b
|
||||
|
||||
! Double precision numbers
|
||||
|
||||
double precision :: rsfac,rho,rs,rhoa,rhob,z
|
||||
double precision :: eccoul, ecd, ecz, ecdd, eczd
|
||||
double precision :: eclr
|
||||
rsfac = (3.0d0/(4.0d0*pi))**(1d0/3d0)
|
||||
|
||||
ec = 0.d0
|
||||
! Test on density
|
||||
rho = rho_a + rho_b
|
||||
if (dabs(rho).ge.1.d-12) then
|
||||
|
||||
rs=rsfac/(rho**(1d0/3d0))
|
||||
rhoa=max(rho_a,1.0d-15)
|
||||
rhob=max(rho_b,1.0d-15)
|
||||
z=(rhoa-rhob)/(rhoa+rhob)
|
||||
|
||||
call ecPW(rs,z,eccoul,ecd,ecz,ecdd,eczd)
|
||||
call ecorrlr(rs,z,mu,eclr)
|
||||
ec=(eccoul-eclr)*rho
|
||||
|
||||
endif
|
||||
|
||||
end
|
||||
@ -1,44 +0,0 @@
|
||||
subroutine f_grid(nBas,nO,nGrid,MO,ERI,f)
|
||||
|
||||
! Compute f
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas
|
||||
integer,intent(in) :: nO
|
||||
integer,intent(in) :: nGrid
|
||||
double precision,intent(in) :: MO(nBas,nGrid)
|
||||
double precision,intent(in) :: ERI(nBas,nBas,nBas,nBas)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: p,q
|
||||
integer :: i,j
|
||||
integer :: iG
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: f(nGrid)
|
||||
|
||||
! Initialization
|
||||
|
||||
f(:) = 0d0
|
||||
|
||||
do p=1,nBas
|
||||
do q=1,nBas
|
||||
do i=1,nO
|
||||
do j=1,nO
|
||||
do iG=1,ngrid
|
||||
|
||||
f(iG) = f(iG) + MO(p,iG)*MO(q,iG)*ERI(p,q,i,j)*MO(i,iG)*MO(j,iG)
|
||||
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
end subroutine f_grid
|
||||
@ -1,88 +0,0 @@
|
||||
subroutine fc_srlda(nBas,nGrid,weight,MO,rho,mu,eG0W0)
|
||||
|
||||
! Compute sr-lda ec
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas
|
||||
integer,intent(in) :: nGrid
|
||||
double precision,intent(in) :: weight(nGrid)
|
||||
double precision,intent(in) :: MO(nBas,nGrid)
|
||||
double precision,intent(in) :: rho(nGrid)
|
||||
double precision,intent(in) :: mu(nGrid)
|
||||
double precision,intent(in) :: eG0W0(nBas)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: iG,p
|
||||
double precision :: r,ra,rb,rap,ram
|
||||
double precision :: rs,rsp,rsm
|
||||
double precision :: ec,ecp,ecm,vcup,vcdw
|
||||
double precision,parameter :: delta = 1d-6
|
||||
double precision,allocatable :: de(:)
|
||||
|
||||
! Memory allocation
|
||||
|
||||
allocate(de(nBas))
|
||||
|
||||
! Initialization
|
||||
|
||||
de(:) = 0d0
|
||||
|
||||
do iG=1,ngrid
|
||||
|
||||
r = max(0d0,rho(iG))
|
||||
ra = 0.5d0*r
|
||||
rb = 0.5d0*r
|
||||
|
||||
if(r > threshold) then
|
||||
|
||||
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
|
||||
|
||||
! call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
|
||||
if(abs(ra) > delta) then
|
||||
|
||||
rap = ra + delta
|
||||
ram = ra - delta
|
||||
|
||||
rsp = (4d0*pi*rap/3d0)**(-1d0/3d0)
|
||||
rsm = (4d0*pi*ram/3d0)**(-1d0/3d0)
|
||||
|
||||
! call lsdsr(rsp,0d0,mu(iG),ecp,vcup,vcdw)
|
||||
! call lsdsr(rsm,0d0,mu(iG),ecm,vcup,vcdw)
|
||||
call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
|
||||
|
||||
|
||||
! call ESRC_MD_LDAERF(mu(iG),rap,rb,.true.,ecp)
|
||||
! call ESRC_MD_LDAERF(mu(iG),ram,rb,.true.,ecm)
|
||||
|
||||
! vcup = (ecp - ecm)/(2d0*delta)
|
||||
|
||||
else
|
||||
|
||||
vcup = 0d0
|
||||
|
||||
end if
|
||||
|
||||
do p=1,nBas
|
||||
|
||||
de(p)= de(p) + weight(iG)*vcup*MO(p,iG)**2
|
||||
|
||||
end do
|
||||
|
||||
end if
|
||||
|
||||
end do
|
||||
|
||||
print*, 'Eigenvalues correction from srDFT (in eV)'
|
||||
call matout(nBas,1,de(:)*HaToeV)
|
||||
|
||||
print*, 'Corrected G0W0 eigenvalues (in eV)'
|
||||
call matout(nBas,1,(eG0W0(:) + de(:))*HaToeV)
|
||||
|
||||
|
||||
|
||||
end subroutine fc_srlda
|
||||
@ -1,46 +0,0 @@
|
||||
subroutine mu_grid(nGrid,rho,f,mu)
|
||||
|
||||
! Compute mu
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nGrid
|
||||
double precision,intent(in) :: rho(nGrid)
|
||||
double precision,intent(in) :: f(nGrid)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: iG
|
||||
double precision,parameter :: thres = 1d-10
|
||||
double precision :: n2
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: mu(nGrid)
|
||||
|
||||
! Initialization
|
||||
|
||||
mu(:) = 0d0
|
||||
|
||||
do iG=1,ngrid
|
||||
|
||||
n2 = 0.25d0*rho(iG)**2
|
||||
|
||||
if(abs(n2) > thres) then
|
||||
|
||||
mu(iG) = f(iG)/n2
|
||||
|
||||
else
|
||||
|
||||
mu(iG) = 1d0/thres
|
||||
|
||||
end if
|
||||
|
||||
end do
|
||||
|
||||
mu(:) = 0.5d0*sqrt(pi)*mu(:)
|
||||
|
||||
end subroutine mu_grid
|
||||
@ -1,77 +0,0 @@
|
||||
subroutine quadrature_grid(nRad,nAng,nGrid,root,weight)
|
||||
|
||||
! Build roots and weights of quadrature grid
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nRad,nAng,nGrid
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: i,j,k
|
||||
double precision :: scale
|
||||
double precision,allocatable :: Radius(:)
|
||||
double precision,allocatable :: RadWeight(:)
|
||||
double precision,allocatable :: XYZ(:,:)
|
||||
double precision,allocatable :: XYZWeight(:)
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: root(3,nGrid)
|
||||
double precision,intent(out) :: weight(nGrid)
|
||||
|
||||
! Memory allocation
|
||||
|
||||
allocate(Radius(nRad),RadWeight(nRad),XYZ(3,nAng),XYZWeight(nAng))
|
||||
|
||||
! Find the radial grid
|
||||
|
||||
scale = 1d0
|
||||
call EulMac(Radius,RadWeight,nRad,scale)
|
||||
|
||||
write(*,20)
|
||||
write(*,30)
|
||||
write(*,20)
|
||||
do i = 1,nRad
|
||||
write(*,40) i,Radius(i),RadWeight(i)
|
||||
end do
|
||||
write(*,20)
|
||||
write(*,*)
|
||||
|
||||
! Find the angular grid
|
||||
|
||||
call Lebdev(XYZ,XYZWeight,nAng)
|
||||
|
||||
write(*,20)
|
||||
write(*,50)
|
||||
write(*,20)
|
||||
do j = 1,nAng
|
||||
write(*,60) j,(XYZ(k,j),k=1,3), XYZWeight(j)
|
||||
end do
|
||||
write(*,20)
|
||||
|
||||
! Form the roots and weights
|
||||
|
||||
k = 0
|
||||
do i=1,nRad
|
||||
do j=1,nAng
|
||||
k = k + 1
|
||||
root(:,k) = Radius(i)*XYZ(:,j)
|
||||
weight(k) = RadWeight(i)*XYZWeight(j)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Compute values of the basis functions (and the its gradient if required) at each grid point
|
||||
|
||||
20 format(T2,58('-'))
|
||||
30 format(T20,'Radial Quadrature',/, &
|
||||
T6,'I',T26,'Radius',T50,'Weight')
|
||||
40 format(T3,I4,T18,F17.10,T35,F25.10)
|
||||
50 format(T20,'Angular Quadrature',/, &
|
||||
T6,'I',T19,'X',T29,'Y',T39,'Z',T54,'Weight')
|
||||
60 format(T3,I4,T13,3F10.5,T50,F10.5)
|
||||
|
||||
end subroutine quadrature_grid
|
||||
@ -1,169 +0,0 @@
|
||||
subroutine read_F12_integrals(nBas,S,C,F,Y,FC)
|
||||
|
||||
! Read one- and two-electron integrals from files
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas
|
||||
double precision,intent(in) :: S(nBas,nBas)
|
||||
|
||||
! Local variables
|
||||
|
||||
logical :: debug
|
||||
integer :: mu,nu,la,si,ka,ta
|
||||
double precision :: ERI,F12,Yuk,F13C12,ExpS
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: C(nBas,nBas,nBas,nBas)
|
||||
double precision,intent(out) :: F(nBas,nBas,nBas,nBas)
|
||||
double precision,intent(out) :: Y(nBas,nBas,nBas,nBas)
|
||||
double precision,intent(out) :: FC(nBas,nBas,nBas,nBas,nBas,nBas)
|
||||
|
||||
debug = .false.
|
||||
|
||||
! Open file with integrals
|
||||
|
||||
open(unit=21,file='int/ERI.dat')
|
||||
open(unit=22,file='int/F12.dat')
|
||||
open(unit=23,file='int/Yuk.dat')
|
||||
open(unit=31,file='int/3eInt_Type1.dat')
|
||||
|
||||
! Read 1/r12 integrals
|
||||
|
||||
C = 0d0
|
||||
do
|
||||
read(21,*,end=21) mu,nu,la,si,ERI
|
||||
! <12|34>
|
||||
C(mu,nu,la,si) = ERI
|
||||
! <32|14>
|
||||
C(la,nu,mu,si) = ERI
|
||||
! <14|32>
|
||||
C(mu,si,la,nu) = ERI
|
||||
! <34|12>
|
||||
C(la,si,mu,nu) = ERI
|
||||
! <41|23>
|
||||
C(si,mu,nu,la) = ERI
|
||||
! <23|41>
|
||||
C(nu,la,si,mu) = ERI
|
||||
! <21|43>
|
||||
C(nu,mu,si,la) = ERI
|
||||
! <43|21>
|
||||
C(si,la,nu,mu) = ERI
|
||||
enddo
|
||||
21 close(unit=21)
|
||||
|
||||
! Read f12 integrals
|
||||
|
||||
F = 0d0
|
||||
do
|
||||
read(22,*,end=22) mu,nu,la,si,F12
|
||||
! <12|34>
|
||||
F(mu,nu,la,si) = F12
|
||||
! <32|14>
|
||||
F(la,nu,mu,si) = F12
|
||||
! <14|32>
|
||||
F(mu,si,la,nu) = F12
|
||||
! <34|12>
|
||||
F(la,si,mu,nu) = F12
|
||||
! <41|23>
|
||||
F(si,mu,nu,la) = F12
|
||||
! <23|41>
|
||||
F(nu,la,si,mu) = F12
|
||||
! <21|43>
|
||||
F(nu,mu,si,la) = F12
|
||||
! <43|21>
|
||||
F(si,la,nu,mu) = F12
|
||||
enddo
|
||||
22 close(unit=22)
|
||||
|
||||
! Read f12/r12 integrals
|
||||
|
||||
Y = 0d0
|
||||
do
|
||||
read(23,*,end=23) mu,nu,la,si,Yuk
|
||||
! <12|34>
|
||||
Y(mu,nu,la,si) = Yuk
|
||||
! <32|14>
|
||||
Y(la,nu,mu,si) = Yuk
|
||||
! <14|32>
|
||||
Y(mu,si,la,nu) = Yuk
|
||||
! <34|12>
|
||||
Y(la,si,mu,nu) = Yuk
|
||||
! <41|23>
|
||||
Y(si,mu,nu,la) = Yuk
|
||||
! <23|41>
|
||||
Y(nu,la,si,mu) = Yuk
|
||||
! <21|43>
|
||||
Y(nu,mu,si,la) = Yuk
|
||||
! <43|21>
|
||||
Y(si,la,nu,mu) = Yuk
|
||||
enddo
|
||||
23 close(unit=23)
|
||||
|
||||
! Read f13/r12 integrals
|
||||
|
||||
FC = 0d0
|
||||
do
|
||||
read(31,*,end=31) mu,nu,la,si,ka,ta,F13C12
|
||||
FC(mu,nu,la,si,ka,ta) = F13C12
|
||||
enddo
|
||||
31 close(unit=31)
|
||||
|
||||
! Print results
|
||||
|
||||
if(debug) then
|
||||
|
||||
write(*,'(A28)') '----------------------'
|
||||
write(*,'(A28)') 'Electron repulsion integrals'
|
||||
write(*,'(A28)') '----------------------'
|
||||
do la=1,nBas
|
||||
do si=1,nBas
|
||||
call matout(nBas,nBas,C(1,1,la,si))
|
||||
enddo
|
||||
enddo
|
||||
write(*,*)
|
||||
|
||||
write(*,'(A28)') '----------------------'
|
||||
write(*,'(A28)') 'F12 integrals'
|
||||
write(*,'(A28)') '----------------------'
|
||||
do la=1,nBas
|
||||
do si=1,nBas
|
||||
call matout(nBas,nBas,F(1,1,la,si))
|
||||
enddo
|
||||
enddo
|
||||
write(*,*)
|
||||
|
||||
write(*,'(A28)') '----------------------'
|
||||
write(*,'(A28)') 'Yukawa integrals'
|
||||
write(*,'(A28)') '----------------------'
|
||||
do la=1,nBas
|
||||
do si=1,nBas
|
||||
call matout(nBas,nBas,Y(1,1,la,si))
|
||||
enddo
|
||||
enddo
|
||||
write(*,*)
|
||||
|
||||
endif
|
||||
|
||||
! Read exponent of Slater geminal
|
||||
open(unit=4,file='input/geminal')
|
||||
read(4,*) ExpS
|
||||
close(unit=4)
|
||||
|
||||
! Transform two-electron integrals
|
||||
|
||||
! do mu=1,nBas
|
||||
! do nu=1,nBas
|
||||
! do la=1,nBas
|
||||
! do si=1,nBas
|
||||
! F(mu,nu,la,si) = (S(mu,la)*S(nu,si) - F(mu,nu,la,si))/ExpS
|
||||
! Y(mu,nu,la,si) = (C(mu,nu,la,si) - Y(mu,nu,la,si))/ExpS
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
|
||||
end subroutine read_F12_integrals
|
||||
@ -1,47 +0,0 @@
|
||||
subroutine read_grid(SGn,nRad,nAng,nGrid)
|
||||
|
||||
! Read grid type
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: SGn
|
||||
|
||||
! Output variables
|
||||
|
||||
integer,intent(out) :: nRad
|
||||
integer,intent(out) :: nAng
|
||||
integer,intent(out) :: nGrid
|
||||
|
||||
write(*,*)'----------------------------------------------------------'
|
||||
write(*,'(A22,I1)')' Quadrature grid: SG-',SGn
|
||||
write(*,*)'----------------------------------------------------------'
|
||||
|
||||
select case (SGn)
|
||||
|
||||
case(0)
|
||||
nRad = 23
|
||||
nAng = 170
|
||||
|
||||
case(1)
|
||||
nRad = 50
|
||||
nAng = 194
|
||||
|
||||
case(2)
|
||||
nRad = 75
|
||||
nAng = 302
|
||||
|
||||
case(3)
|
||||
nRad = 99
|
||||
nAng = 590
|
||||
|
||||
case default
|
||||
call print_warning('!!! Quadrature grid not available !!!')
|
||||
stop
|
||||
|
||||
end select
|
||||
|
||||
nGrid = nRad*nAng
|
||||
|
||||
end subroutine read_grid
|
||||
BIN
src/IntPak.tgz
BIN
src/IntPak.tgz
Binary file not shown.
@ -1,108 +0,0 @@
|
||||
subroutine AO_values(doDrift,nBas,nShell,nWalk,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,r,AO,dAO)
|
||||
|
||||
! Compute values of the AOs and their derivatives (if required)
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
logical,intent(in) :: doDrift
|
||||
integer,intent(in) :: nBas,nShell,nWalk
|
||||
double precision,intent(in) :: CenterShell(maxShell,3)
|
||||
integer,intent(in) :: TotAngMomShell(maxShell),KShell(maxShell)
|
||||
double precision,intent(in) :: DShell(maxShell,maxK),ExpShell(maxShell,maxK)
|
||||
double precision,intent(in) :: r(nWalk,2,3)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: atot,nShellFunction,a(3)
|
||||
integer,allocatable :: ShellFunction(:,:)
|
||||
double precision :: rASq,xA,yA,zA,norm_coeff,prim
|
||||
|
||||
integer :: iSh,iShF,iK,iW,iEl,iBas,ixyz
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: AO(nWalk,2,nBas),dAO(nWalk,2,3,nBas)
|
||||
|
||||
! Initialization
|
||||
|
||||
AO = 0d0
|
||||
if(doDrift) dAO = 0d0
|
||||
iBas = 0
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Loops over shells
|
||||
!------------------------------------------------------------------------
|
||||
do iSh=1,nShell
|
||||
|
||||
atot = TotAngMomShell(iSh)
|
||||
nShellFunction = (atot*atot + 3*atot + 2)/2
|
||||
allocate(ShellFunction(1:nShellFunction,1:3))
|
||||
call generate_shell(atot,nShellFunction,ShellFunction)
|
||||
|
||||
do iShF=1,nShellFunction
|
||||
|
||||
iBas = iBas + 1
|
||||
a(1) = ShellFunction(iShF,1)
|
||||
a(2) = ShellFunction(iShF,2)
|
||||
a(3) = ShellFunction(iShF,3)
|
||||
|
||||
do iW=1,nWalk
|
||||
do iEl=1,2
|
||||
|
||||
xA = r(iW,iEl,1) - CenterShell(iSh,1)
|
||||
yA = r(iW,iEl,2) - CenterShell(iSh,2)
|
||||
zA = r(iW,iEl,3) - CenterShell(iSh,3)
|
||||
|
||||
! Calculate distance for exponential
|
||||
|
||||
rASq = xA**2 + yA**2 + zA**2
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Loops over contraction degrees
|
||||
!-------------------------------------------------------------------------
|
||||
do iK=1,KShell(iSh)
|
||||
|
||||
! Calculate the exponential part
|
||||
prim = DShell(iSh,iK)*norm_coeff(ExpShell(iSh,iK),a)*exp(-ExpShell(iSh,iK)*rASq)
|
||||
AO(iW,iEl,iBas) = AO(iW,iEl,iBas) + prim
|
||||
|
||||
if(doDrift) then
|
||||
prim = -2d0*ExpShell(iSh,iK)*prim
|
||||
do ixyz=1,3
|
||||
dAO(iW,iEl,ixyz,iBas) = dAO(iW,iEl,ixyz,iBas) + prim
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
|
||||
if(doDrift) then
|
||||
|
||||
dAO(iW,iEl,1,iBas) = xA**(a(1)+1)*yA**a(2)*zA**a(3)*dAO(iW,iEl,1,iBas)
|
||||
if(a(1) > 0) dAO(iW,iEl,1,iBas) = dAO(iW,iEl,1,iBas) + dble(a(1))*xA**(a(1)-1)*yA**a(2)*zA**a(3)*AO(iW,iEl,iBas)
|
||||
|
||||
dAO(iW,iEl,2,iBas) = xA**a(1)*yA**(a(2)+1)*zA**a(3)*dAO(iW,iEl,2,iBas)
|
||||
if(a(2) > 0) dAO(iW,iEl,2,iBas) = dAO(iW,iEl,2,iBas) + dble(a(2))*xA**a(1)*yA**(a(2)-1)*zA**a(3)*AO(iW,iEl,iBas)
|
||||
|
||||
dAO(iW,iEl,3,iBas) = xA**a(1)*yA**a(2)*zA**(a(3)+1)*dAO(iW,iEl,3,iBas)
|
||||
if(a(3) > 0) dAO(iW,iEl,3,iBas) = dAO(iW,iEl,3,iBas) + dble(a(3))*xA**a(1)*yA**a(2)*zA**(a(3)-1)*AO(iW,iEl,iBas)
|
||||
|
||||
endif
|
||||
|
||||
! Calculate polynmial part
|
||||
|
||||
AO(iW,iEl,iBas) = xA**a(1)*yA**a(2)*zA**a(3)*AO(iW,iEl,iBas)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
|
||||
enddo
|
||||
deallocate(ShellFunction)
|
||||
enddo
|
||||
!------------------------------------------------------------------------
|
||||
! End loops over shells
|
||||
!------------------------------------------------------------------------
|
||||
|
||||
end subroutine AO_values
|
||||
@ -1,101 +0,0 @@
|
||||
subroutine AO_values_grid(nBas,nShell,CenterShell,TotAngMomShell,KShell,DShell,ExpShell, &
|
||||
nGrid,root,AO,dAO)
|
||||
|
||||
! Compute values of the AOs and their derivatives with respect to the cartesian coordinates
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas,nShell
|
||||
double precision,intent(in) :: CenterShell(maxShell,3)
|
||||
integer,intent(in) :: TotAngMomShell(maxShell)
|
||||
integer,intent(in) :: KShell(maxShell)
|
||||
double precision,intent(in) :: DShell(maxShell,maxK)
|
||||
double precision,intent(in) :: ExpShell(maxShell,maxK)
|
||||
double precision,intent(in) :: root(3,nGrid)
|
||||
integer,intent(in) :: nGrid
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: atot,nShellFunction,a(3)
|
||||
integer,allocatable :: ShellFunction(:,:)
|
||||
double precision :: rASq,xA,yA,zA,norm_coeff,prim
|
||||
|
||||
integer :: iSh,iShF,iK,iG,iBas
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: AO(nBas,nGrid)
|
||||
double precision,intent(out) :: dAO(3,nBas,nGrid)
|
||||
|
||||
! Initialization
|
||||
|
||||
iBas = 0
|
||||
AO(:,:) = 0d0
|
||||
dAO(:,:,:) = 0d0
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Loops over shells
|
||||
!------------------------------------------------------------------------
|
||||
do iSh=1,nShell
|
||||
|
||||
atot = TotAngMomShell(iSh)
|
||||
nShellFunction = (atot*atot + 3*atot + 2)/2
|
||||
allocate(ShellFunction(1:nShellFunction,1:3))
|
||||
call generate_shell(atot,nShellFunction,ShellFunction)
|
||||
|
||||
do iShF=1,nShellFunction
|
||||
|
||||
iBas = iBas + 1
|
||||
a(:) = ShellFunction(iShF,:)
|
||||
|
||||
do iG=1,nGrid
|
||||
|
||||
xA = root(1,iG) - CenterShell(iSh,1)
|
||||
yA = root(2,iG) - CenterShell(iSh,2)
|
||||
zA = root(3,iG) - CenterShell(iSh,3)
|
||||
|
||||
! Calculate distance for exponential
|
||||
|
||||
rASq = xA**2 + yA**2 + zA**2
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Loops over contraction degrees
|
||||
!-------------------------------------------------------------------------
|
||||
do iK=1,KShell(iSh)
|
||||
|
||||
! Calculate the exponential part
|
||||
|
||||
prim = DShell(iSh,iK)*norm_coeff(ExpShell(iSh,iK),a)*exp(-ExpShell(iSh,iK)*rASq)
|
||||
AO(iBas,iG) = AO(iBas,iG) + prim
|
||||
|
||||
prim = -2d0*ExpShell(iSh,iK)*prim
|
||||
dAO(:,iBas,iG) = dAO(:,iBas,iG) + prim
|
||||
|
||||
enddo
|
||||
|
||||
dAO(1,iBas,iG) = xA**(a(1)+1)*yA**a(2)*zA**a(3)*dAO(1,iBas,iG)
|
||||
if(a(1) > 0) dAO(1,iBas,iG) = dAO(1,iBas,iG) + dble(a(1))*xA**(a(1)-1)*yA**a(2)*zA**a(3)*AO(iBas,iG)
|
||||
|
||||
dAO(2,iBas,iG) = xA**a(1)*yA**(a(2)+1)*zA**a(3)*dAO(2,iBas,iG)
|
||||
if(a(2) > 0) dAO(2,iBas,iG) = dAO(2,iBas,iG) + dble(a(2))*xA**a(1)*yA**(a(2)-1)*zA**a(3)*AO(iBas,iG)
|
||||
|
||||
dAO(3,iBas,iG) = xA**a(1)*yA**a(2)*zA**(a(3)+1)*dAO(3,iBas,iG)
|
||||
if(a(3) > 0) dAO(3,iBas,iG) = dAO(3,iBas,iG) + dble(a(3))*xA**a(1)*yA**a(2)*zA**(a(3)-1)*AO(iBas,iG)
|
||||
|
||||
! Calculate polynmial part
|
||||
|
||||
AO(iBas,iG) = xA**a(1)*yA**a(2)*zA**a(3)*AO(iBas,iG)
|
||||
|
||||
enddo
|
||||
|
||||
enddo
|
||||
deallocate(ShellFunction)
|
||||
enddo
|
||||
!------------------------------------------------------------------------
|
||||
! End loops over shells
|
||||
!------------------------------------------------------------------------
|
||||
|
||||
end subroutine AO_values_grid
|
||||
@ -1,65 +0,0 @@
|
||||
subroutine Green_function(nBas,nO,nV,nWalk,nWP,cO,cV,eO_Quad,eV_Quad,AO, &
|
||||
o1MO,o2MO,v1MO,v2MO,o11,o12,o21,o22,v11,v12,v21,v22)
|
||||
|
||||
! Calculate the Green functions
|
||||
|
||||
implicit none
|
||||
|
||||
include 'parameters.h'
|
||||
include 'quadrature.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas,nO,nV,nWalk,nWP
|
||||
double precision,intent(in) :: AO(nWalk,2,nBas),cO(nBas,nO),cV(nBas,nV), &
|
||||
eO_Quad(nQuad,nO),eV_Quad(nQuad,nV)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: kW,lW,klW,i,a,q
|
||||
double precision :: o1MO(nWalk,nO),o2MO(nWalk,nO),v1MO(nWalk,nV),v2MO(nWalk,nV)
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: o11(nQuad,nWP),o12(nQuad,nWP),o21(nQuad,nWP),o22(nQuad,nWP)
|
||||
double precision,intent(out) :: v11(nQuad,nWP),v12(nQuad,nWP),v21(nQuad,nWP),v22(nQuad,nWP)
|
||||
|
||||
! Calculate occupied and virtual MOs
|
||||
|
||||
o1MO = matmul(AO(:,1,:),cO)
|
||||
o2MO = matmul(AO(:,2,:),cO)
|
||||
v1MO = matmul(AO(:,1,:),cV)
|
||||
v2MO = matmul(AO(:,2,:),cV)
|
||||
|
||||
! Compute occupied Green functions
|
||||
o11 = 0d0
|
||||
o12 = 0d0
|
||||
o21 = 0d0
|
||||
o22 = 0d0
|
||||
v11 = 0d0
|
||||
v12 = 0d0
|
||||
v21 = 0d0
|
||||
v22 = 0d0
|
||||
|
||||
do q=1,nQuad
|
||||
klW = 0
|
||||
do kW=1,nWalk-1
|
||||
do lW=kW+1,nWalk
|
||||
klW = klW + 1
|
||||
do i=1,nO
|
||||
o11(q,klW) = o11(q,klW) + o1MO(kW,i)*o1MO(lW,i)*eO_Quad(q,i)
|
||||
o12(q,klW) = o12(q,klW) + o1MO(kW,i)*o2MO(lW,i)*eO_Quad(q,i)
|
||||
o21(q,klW) = o21(q,klW) + o2MO(kW,i)*o1MO(lW,i)*eO_Quad(q,i)
|
||||
o22(q,klW) = o22(q,klW) + o2MO(kW,i)*o2MO(lW,i)*eO_Quad(q,i)
|
||||
enddo
|
||||
do a=1,nV
|
||||
v11(q,klW) = v11(q,klW) + v1MO(kW,a)*v1MO(lW,a)*eV_Quad(q,a)
|
||||
v12(q,klW) = v12(q,klW) + v1MO(kW,a)*v2MO(lW,a)*eV_Quad(q,a)
|
||||
v21(q,klW) = v21(q,klW) + v2MO(kW,a)*v1MO(lW,a)*eV_Quad(q,a)
|
||||
v22(q,klW) = v22(q,klW) + v2MO(kW,a)*v2MO(lW,a)*eV_Quad(q,a)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
end subroutine Green_function
|
||||
344
src/MC/MCMP2.f90
344
src/MC/MCMP2.f90
@ -1,344 +0,0 @@
|
||||
subroutine MCMP2(doDrift,nBas,nC,nO,nV,c,e,EcMP2, &
|
||||
nMC,nEq,nWalk,dt,nPrint, &
|
||||
nShell,CenterShell,TotAngMomShell,KShell,DShell,ExpShell, &
|
||||
Norm, &
|
||||
EcMCMP2,Err_EcMCMP2,Var_EcMCMP2)
|
||||
|
||||
! Perform Monte Carlo MP2 calculation
|
||||
|
||||
implicit none
|
||||
|
||||
include 'parameters.h'
|
||||
include 'quadrature.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
logical,intent(in) :: doDrift
|
||||
integer,intent(in) :: nBas,nC,nO,nV,nMC,nEq,nWalk,nPrint
|
||||
double precision,intent(inout):: dt
|
||||
double precision,intent(in) :: EcMP2(3)
|
||||
double precision,intent(in) :: c(nBas,nBas),e(nBas)
|
||||
|
||||
integer,intent(in) :: nShell
|
||||
integer,intent(in) :: TotAngMomShell(maxShell),KShell(maxShell)
|
||||
double precision,intent(in) :: CenterShell(maxShell,3),DShell(maxShell,maxK),ExpShell(maxShell,maxK)
|
||||
|
||||
! Local variables
|
||||
|
||||
logical :: AcPh,EqPh,Accept,dump
|
||||
double precision :: start_Eq,end_Eq,t_Eq,start_Ac,end_Ac,t_Ac
|
||||
integer :: nWP
|
||||
double precision :: Norm,NormSq,nData,tau
|
||||
double precision,allocatable :: chi1(:,:,:),chi2(:,:,:),eta(:)
|
||||
|
||||
double precision,allocatable :: cO(:,:),cV(:,:),eO(:),eV(:),P(:,:),eO_Quad(:,:),eV_Quad(:,:)
|
||||
double precision,allocatable :: r(:,:,:), r12(:), gAO(:,:,:), g(:,:), w(:)
|
||||
double precision,allocatable :: rp(:,:,:),r12p(:),gAOp(:,:,:), gp(:,:),wp(:)
|
||||
double precision,allocatable :: o1MO(:,:),o2MO(:,:),v1MO(:,:),v2MO(:,:)
|
||||
double precision,allocatable :: o11(:,:),o12(:,:),o21(:,:),o22(:,:)
|
||||
double precision,allocatable :: v11(:,:),v12(:,:),v21(:,:),v22(:,:)
|
||||
double precision,allocatable :: fd_Quad(:,:),fx_Quad(:,:),fd(:),fx(:),fdx(:)
|
||||
|
||||
double precision,allocatable :: dgAO(:,:,:,:),dg(:,:,:),dgAOp(:,:,:,:),dgp(:,:,:)
|
||||
double precision,allocatable :: F(:,:,:),Fp(:,:,:),T(:),Tp(:)
|
||||
|
||||
double precision :: acceptance,D
|
||||
double precision :: eloc_MP2(3),mean_MP2(3),variance_MP2(3)
|
||||
|
||||
integer :: iW,kW,lW,klW,iMC,q
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: EcMCMP2(3),Err_EcMCMP2(3),Var_EcMCMP2(3)
|
||||
|
||||
! Number of distinct walker pairs
|
||||
|
||||
nWP = nWalk*(nWalk-1)/2
|
||||
|
||||
! Diffusion coefficient
|
||||
|
||||
D = 0.5d0
|
||||
|
||||
! Do diffusion-drift moves?
|
||||
|
||||
if(doDrift) then
|
||||
|
||||
write(*,*)
|
||||
write(*,*) '*** Diffusion-drift algorithm ***'
|
||||
write(*,*)
|
||||
|
||||
else
|
||||
|
||||
write(*,*)
|
||||
write(*,*) '*** Diffusion-only algorithm ***'
|
||||
write(*,*)
|
||||
|
||||
endif
|
||||
|
||||
! Print results
|
||||
|
||||
dump = .true.
|
||||
if(dump) open(unit=13,file='results/data')
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Memory allocation
|
||||
!------------------------------------------------------------------------
|
||||
allocate(cO(nBas,nO),cV(nBas,nV),eO(nO),eV(nV), &
|
||||
eO_Quad(nQuad,nO),eV_Quad(nQuad,nV), &
|
||||
P(nBas,nBas),r(nWalk,2,3),rp(nWalk,2,3), &
|
||||
chi1(nWalk,2,3),chi2(nWalk,2,3),eta(nWalk), &
|
||||
r12(nWalk),r12p(nWalk),w(nWalk),wp(nWalk), &
|
||||
g(nWalk,2),gp(nWalk,2),gAO(nWalk,2,nBas),gAOp(nWalk,2,nBas), &
|
||||
dg(nWalk,2,3),dgp(nWalk,2,3),dgAO(nWalk,2,3,nBas),dgAOp(nWalk,2,3,nBas), &
|
||||
o1MO(nWalk,nO),v1MO(nWalk,nV),o2MO(nWalk,nO),v2MO(nWalk,nV), &
|
||||
o11(nQuad,nWP),v11(nQuad,nWP),o12(nQuad,nWP),v12(nQuad,nWP), &
|
||||
o21(nQuad,nWP),v21(nQuad,nWP),o22(nQuad,nWP),v22(nQuad,nWP), &
|
||||
fd_Quad(nQuad,nWP),fd(nWP),fx_Quad(nQuad,nWP),fx(nWP),fdx(nWP), &
|
||||
T(nWalk),Tp(nWalk),F(nWalk,2,3),Fp(nWalk,2,3))
|
||||
|
||||
! Split MOs into occupied and virtual sets
|
||||
|
||||
eO(1:nO) = e(nC+1:nC+nO)
|
||||
eV(1:nV) = e(nC+nO+1:nBas)
|
||||
|
||||
do q=1,nQuad
|
||||
tau = 1d0/rQuad(q)
|
||||
eO_Quad(q,1:nO) = exp(+eO(1:nO)*(tau-1d0))*sqrt(tau)
|
||||
eV_Quad(q,1:nV) = exp(-eV(1:nV)*(tau-1d0))*sqrt(tau)
|
||||
enddo
|
||||
|
||||
cO(1:nBas,1:nO) = c(1:nBas,nC+1:nC+nO)
|
||||
cV(1:nBas,1:nV) = c(1:nBas,nC+nO+1:nBas)
|
||||
|
||||
! Compute norm of the trial wave function
|
||||
|
||||
call norm_trial(nBas,nO,cO,P,Norm,NormSq)
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Initialize MC-MP2 calculation
|
||||
!------------------------------------------------------------------------
|
||||
|
||||
! Initialize electron coordinates
|
||||
|
||||
call random_number(r)
|
||||
r = 2d0*r - 1d0
|
||||
|
||||
! Compute initial interelectronic distances
|
||||
|
||||
call rij(nWalk,r,r12)
|
||||
|
||||
! Compute initial AO values and their derivatives (if required)
|
||||
|
||||
call AO_values(doDrift,nBas,nShell,nWalk,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,r,gAO,dgAO)
|
||||
|
||||
! Compute initial weight function
|
||||
|
||||
call density(doDrift,nBas,nWalk,P,gAO,dgAO,g,dg)
|
||||
|
||||
! Compute initial weights
|
||||
|
||||
w(1:nWalk) = g(1:nWalk,1)*g(1:nWalk,2)/r12(1:nWalk)
|
||||
|
||||
! Compute initial quantum force
|
||||
|
||||
if(doDrift) call drift(nWalk,r,r12,g,dg,F)
|
||||
|
||||
! Equilibration or Accumulation?
|
||||
|
||||
AcPh = .false.
|
||||
EqPh = .true.
|
||||
|
||||
! Initialization
|
||||
|
||||
nData = 0d0
|
||||
acceptance = 0d0
|
||||
|
||||
mean_MP2 = 0d0
|
||||
variance_MP2 = 0d0
|
||||
|
||||
T = 1d0
|
||||
Tp = 1d0
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Start main Monte Carlo loop
|
||||
!------------------------------------------------------------------------
|
||||
call cpu_time(start_Eq)
|
||||
|
||||
do iMC=1,nEq+nMC
|
||||
|
||||
! Timings
|
||||
|
||||
if(iMC == nEq + 1) then
|
||||
AcPh = .true.
|
||||
EqPh = .false.
|
||||
write(*,*) 'Time step value at the end of equilibration: dt = ',dt
|
||||
write(*,*)
|
||||
call cpu_time(end_Eq)
|
||||
t_Eq = end_Eq - start_Eq
|
||||
write(*,*)
|
||||
write(*,'(A65,1X,F9.3,A8)') 'Total CPU time for equilibration = ',t_Eq,' seconds'
|
||||
write(*,*)
|
||||
call cpu_time(start_Ac)
|
||||
endif
|
||||
|
||||
! Optimize time step to reach 50% acceptance
|
||||
|
||||
if(EqPh .and. mod(iMC,100) == 0) call optimize_timestep(nWalk,iMC,acceptance,dt)
|
||||
|
||||
! Move electrons
|
||||
|
||||
call random_number(chi1)
|
||||
call random_number(chi2)
|
||||
|
||||
! Diffusion
|
||||
|
||||
rp(:,:,:) = r(:,:,:) + sqrt(2d0*D*dt)*sqrt(-2d0*log(chi1(:,:,:)))*cos(2d0*pi*chi2(:,:,:))
|
||||
|
||||
! Drift
|
||||
|
||||
if(doDrift) rp(:,:,:) = rp(:,:,:) + D*dt*F(:,:,:)
|
||||
|
||||
! Compute new interelectronic distances
|
||||
|
||||
call rij(nWalk,rp,r12p)
|
||||
|
||||
! Compute new AO values and their derivatives (if required)
|
||||
|
||||
call AO_values(doDrift,nBas,nShell,nWalk,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,rp,gAOp,dgAOp)
|
||||
|
||||
call Density(doDrift,nBas,nWalk,P,gAOp,dgAOp,gp,dgp)
|
||||
|
||||
! Compute new weights
|
||||
|
||||
wp(1:nWalk) = gp(1:nWalk,1)*gp(1:nWalk,2)/r12p(1:nWalk)
|
||||
|
||||
! Compute new quantum force and transition probability
|
||||
|
||||
if(doDrift) then
|
||||
|
||||
call Drift(nWalk,rp,r12p,gp,dgp,Fp)
|
||||
call transition_probability(nWalk,dt,D,r,rp,F,Fp,T,Tp)
|
||||
|
||||
endif
|
||||
|
||||
! Move for walkers
|
||||
|
||||
call random_number(eta)
|
||||
|
||||
do iW=1,nWalk
|
||||
|
||||
Accept = (wp(iW)*Tp(iW))/(w(iW)*T(iW)) > eta(iW)
|
||||
|
||||
if(Accept) then
|
||||
|
||||
acceptance = acceptance + 1d0
|
||||
|
||||
r(iW,1:2,1:3) = rp(iW,1:2,1:3)
|
||||
gAO(iW,1:2,1:nBas) = gAOp(iW,1:2,1:nBas)
|
||||
r12(iW) = r12p(iW)
|
||||
w(iW) = wp(iW)
|
||||
|
||||
if(doDrift) F(iW,1:2,1:3) = Fp(iW,1:2,1:3)
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
|
||||
! Accumulation phase
|
||||
|
||||
if(AcPh) then
|
||||
|
||||
nData = nData + 1d0
|
||||
|
||||
! Calculate Green functions
|
||||
|
||||
call Green_function(nBas,nO,nV,nWalk,nWP,cO,cV,eO_Quad,eV_Quad,gAO, &
|
||||
o1MO,o2MO,v1MO,v2MO,o11,o12,o21,o22,v11,v12,v21,v22)
|
||||
|
||||
! Compute local energy
|
||||
|
||||
fd_Quad = o11*o22*v11*v22 + o12*o21*v12*v21
|
||||
fx_Quad = o11*o22*v12*v21 + o12*o21*v11*v22
|
||||
|
||||
fd = matmul(wQuad,fd_Quad)
|
||||
fx = matmul(wQuad,fx_Quad)
|
||||
|
||||
eloc_MP2 = 0d0
|
||||
klW = 0
|
||||
do kW=1,nWalk-1
|
||||
do lW=kW+1,nWalk
|
||||
klW = klW + 1
|
||||
eloc_MP2(2) = eloc_MP2(2) + fd(klW)/(r12(kW)*r12(lW)*w(kW)*w(lW))
|
||||
eloc_MP2(3) = eloc_MP2(3) + fx(klW)/(r12(kW)*r12(lW)*w(kW)*w(lW))
|
||||
enddo
|
||||
enddo
|
||||
|
||||
eloc_MP2(2) = -2d0*eloc_MP2(2)/dble(2*nWP)
|
||||
eloc_MP2(3) = eloc_MP2(3)/dble(2*nWP)
|
||||
|
||||
fdx = -2d0*fd + fx
|
||||
eloc_MP2(1) = eloc_MP2(2) + eloc_MP2(3)
|
||||
|
||||
! Accumulate results
|
||||
|
||||
mean_MP2 = mean_MP2 + eloc_MP2
|
||||
variance_MP2 = variance_MP2 + eloc_MP2*eloc_MP2
|
||||
|
||||
! Print results
|
||||
|
||||
if(mod(iMC,nPrint) == 0) then
|
||||
|
||||
call compute_error(nData,mean_MP2,variance_MP2,Err_EcMCMP2)
|
||||
EcMCMP2 = mean_MP2/nData
|
||||
Var_EcMCMP2 = variance_MP2/nData
|
||||
EcMCMP2 = Norm*EcMCMP2
|
||||
Var_EcMCMP2 = Norm*Var_EcMCMP2
|
||||
Err_EcMCMP2 = Norm*Err_EcMCMP2
|
||||
|
||||
write(*,*)
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
write(*,'(1X,A36,1X,A1,1X,I15)') 'Number of data points ','|',int(nData)
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
write(*,'(1X,A36,1X,A1,1X,10I15)') 'acceptance ','|',int(100*acceptance/dble(nWalk*iMC))
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') 'MP2 correlation energy Total ','|',EcMCMP2(1)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Direct ','|',EcMCMP2(2)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Exchange ','|',EcMCMP2(3)
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') 'Statistical error Total ','|',Err_EcMCMP2(1)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Direct ','|',Err_EcMCMP2(2)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Exchange ','|',Err_EcMCMP2(3)
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') 'Variance Total ','|',Var_EcMCMP2(1)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Direct ','|',Var_EcMCMP2(2)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Exchange ','|',Var_EcMCMP2(3)
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') 'Dev. wrt deterministic Total ','|',EcMCMP2(1) - EcMP2(1)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Direct ','|',EcMCMP2(2) - EcMP2(2)
|
||||
write(*,'(1X,A36,1X,A1,1X,10F15.8)') ' Exchange ','|',EcMCMP2(3) - EcMP2(3)
|
||||
write(*,*)'-------------------------------------------------------'
|
||||
|
||||
if(dump) write(13,*) int(nData),EcMCMP2(1),Err_EcMCMP2(1)
|
||||
|
||||
endif
|
||||
|
||||
endif
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! End main Monte Carlo loop
|
||||
!------------------------------------------------------------------------
|
||||
enddo
|
||||
|
||||
! Timing
|
||||
|
||||
call cpu_time(end_Ac)
|
||||
t_Ac = end_Ac - start_Ac
|
||||
write(*,*)
|
||||
write(*,'(A65,1X,F9.3,A8)') 'Total CPU time for accumulation = ',t_Ac,' seconds'
|
||||
write(*,*)
|
||||
|
||||
! Close files
|
||||
|
||||
if(dump) close(unit=13)
|
||||
|
||||
end subroutine MCMP2
|
||||
@ -1,44 +0,0 @@
|
||||
subroutine MO_values_grid(nBas,nGrid,c,AO,dAO,MO,dMO)
|
||||
|
||||
! Compute values of the MOs and their derivatives with respect to the cartesian coordinates
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas
|
||||
integer,intent(in) :: nGrid
|
||||
double precision,intent(in) :: c(nBas,nBas)
|
||||
double precision,intent(in) :: AO(nBas,nGrid)
|
||||
double precision,intent(in) :: dAO(ncart,nBas,nGrid)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: p,mu,iG
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: MO(nBas,nGrid)
|
||||
double precision,intent(out) :: dMO(ncart,nBas,nGrid)
|
||||
|
||||
! Initialization
|
||||
|
||||
MO(:,:) = 0d0
|
||||
dMO(:,:,:) = 0d0
|
||||
|
||||
do p=1,nBas
|
||||
do mu=1,nBas
|
||||
do iG=1,ngrid
|
||||
|
||||
MO(p,iG) = MO(p,iG) + c(mu,p)*AO(mu,iG)
|
||||
|
||||
dMO(1,p,iG) = dMO(1,p,iG) + c(mu,p)*dAO(1,mu,iG)
|
||||
dMO(2,p,iG) = dMO(2,p,iG) + c(mu,p)*dAO(2,mu,iG)
|
||||
dMO(3,p,iG) = dMO(3,p,iG) + c(mu,p)*dAO(3,mu,iG)
|
||||
|
||||
end do
|
||||
end do
|
||||
end do
|
||||
|
||||
end subroutine MO_values_grid
|
||||
@ -1,10 +0,0 @@
|
||||
default:
|
||||
ninja
|
||||
make -C ..
|
||||
|
||||
clean:
|
||||
ninja -t clean
|
||||
|
||||
debug:
|
||||
ninja -t clean
|
||||
make -C .. debug
|
||||
@ -1,121 +0,0 @@
|
||||
subroutine MinMCMP2(nBas,nEl,nC,nO,nV,c,e,EcMP2, &
|
||||
nMC,nEq,nWalk,dt,nPrint, &
|
||||
nShell,CenterShell,TotAngMomShell,KShell,DShell,ExpShell, &
|
||||
TrialType,Norm,cTrial,gradient,hessian)
|
||||
|
||||
! Minimize the variance of MC-MP2
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas,nEl,nC,nO,nV,nMC,nEq,nWalk,nPrint
|
||||
double precision,intent(in) :: EcMP2(3),dt
|
||||
double precision,intent(in) :: c(nBas,nBas),e(nBas)
|
||||
|
||||
integer,intent(in) :: nShell
|
||||
integer,intent(in) :: TotAngMomShell(maxShell),KShell(maxShell)
|
||||
double precision,intent(in) :: CenterShell(maxShell,3),DShell(maxShell,maxK),ExpShell(maxShell,maxK)
|
||||
|
||||
! Local variables
|
||||
|
||||
logical :: debug,varmin,mincvg
|
||||
double precision :: thresh
|
||||
double precision,allocatable :: max_gradient(:),energy_MCMP2(:),variance_MCMP2(:),error_MCMP2(:),NormTr(:)
|
||||
|
||||
double precision :: EcMCMP2(3),Err_EcMCMP2(3),Var_EcMCMP2(3)
|
||||
|
||||
integer :: it,nIt,i
|
||||
|
||||
! Output variables
|
||||
|
||||
integer,intent(in) :: TrialType
|
||||
double precision,intent(inout):: Norm,cTrial(nBas),gradient(nBas),hessian(nBas,nBas)
|
||||
|
||||
! Debuging mode
|
||||
|
||||
! debug = .true.
|
||||
debug = .false.
|
||||
|
||||
! Minimization parameters
|
||||
|
||||
varmin = .true.
|
||||
mincvg = .false.
|
||||
nIt = 10
|
||||
thresh = 1d-5
|
||||
allocate(max_gradient(nIt),energy_MCMP2(nIt),variance_MCMP2(nIt),error_MCMP2(nIt),normTr(nIt))
|
||||
|
||||
if(TrialType == 1) then
|
||||
|
||||
! Use HOMO as guess
|
||||
cTrial(1:nBas) = c(1:nBas,nEl/2)
|
||||
! Normalization factor will be computed later
|
||||
|
||||
endif
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! Start MC-MP2 variance minimization
|
||||
!------------------------------------------------------------------------
|
||||
it = 0
|
||||
do while (it < nIt .and. .not.(mincvg))
|
||||
|
||||
it = it + 1
|
||||
|
||||
write(*,*) '**********************************************************************'
|
||||
write(*,*) ' Variance minimization of MC-MP2 energy '
|
||||
write(*,*) '**********************************************************************'
|
||||
write(*,*) ' Iteration n.',it
|
||||
write(*,*) '**********************************************************************'
|
||||
|
||||
write(*,*)
|
||||
write(*,*) ' Trial wave function coefficients at iteration n.',it
|
||||
call matout(nBas,1,cTrial)
|
||||
write(*,*)
|
||||
|
||||
call MCMP2(varmin,nBas,nEl,nC,nO,nV,c,e,EcMP2, &
|
||||
nMC,nEq,nWalk,dt,nPrint, &
|
||||
nShell,CenterShell,TotAngMomShell,KShell,DShell,ExpShell, &
|
||||
TrialType,Norm,cTrial,gradient,hessian, &
|
||||
EcMCMP2,Err_EcMCMP2,Var_EcMCMP2)
|
||||
|
||||
! Newton update of the coefficients
|
||||
|
||||
call Newton(nBas,gradient,hessian,cTrial)
|
||||
|
||||
! Check for convergence
|
||||
|
||||
max_gradient(it) = maxval(abs(gradient))
|
||||
energy_MCMP2(it) = EcMCMP2(1)
|
||||
variance_MCMP2(it) = Var_EcMCMP2(1)
|
||||
error_MCMP2(it) = Err_EcMCMP2(1)
|
||||
NormTr(it) = Norm
|
||||
|
||||
write(*,*)
|
||||
write(*,*) 'Maximum gradient at iteration n.',it,':',max_gradient(it)
|
||||
write(*,*)
|
||||
|
||||
if(max_gradient(it) < thresh) then
|
||||
write(*,*) ' Miracle! Variance minimization of MC-MP2 has converged!'
|
||||
mincvg = .true.
|
||||
endif
|
||||
|
||||
enddo
|
||||
|
||||
write(*,*)
|
||||
write(*,*) '********************************'
|
||||
write(*,*) 'Summary of variance minimization'
|
||||
write(*,*) '********************************'
|
||||
write(*,*)
|
||||
|
||||
write(*,'(A3,A20,A20,A20,A20,A20,A20)') &
|
||||
'It.','Gradient','Ec(MC-MPC2)','Variance','Error','Ec(MC-MP2)-Ec(MP2)','Norm'
|
||||
write(*,'(I3,4X,F16.10,4X,F16.10,4X,F16.10,4X,F16.10,4X,F16.10,4X,F16.10)') &
|
||||
(i,max_gradient(i),energy_MCMP2(i),variance_MCMP2(i),error_MCMP2(i),energy_MCMP2(i)-EcMP2(1),NormTr(i),i=1,it)
|
||||
write(*,*)
|
||||
|
||||
!------------------------------------------------------------------------
|
||||
! End MC-MP2 variance minimization
|
||||
!------------------------------------------------------------------------
|
||||
|
||||
end subroutine MinMCMP2
|
||||
@ -1,67 +0,0 @@
|
||||
subroutine NDrift(nBas,nShell,nWalk,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,P,r,w,F)
|
||||
|
||||
! Compute quantum force numerically
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nWalk,nBas
|
||||
double precision,intent(in) :: P(nBas,nBas),r(nWalk,2,3),w(nWalk)
|
||||
|
||||
integer,intent(in) :: nShell
|
||||
integer,intent(in) :: TotAngMomShell(maxShell),KShell(maxShell)
|
||||
double precision,intent(in) :: CenterShell(maxShell,3),DShell(maxShell,maxK),ExpShell(maxShell,maxK)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: iW,iEl,ixyz
|
||||
double precision :: delta
|
||||
double precision :: wp,wm
|
||||
double precision,allocatable :: rp(:,:,:),rm(:,:,:),r12p(:),r12m(:)
|
||||
double precision,allocatable :: gAOp(:,:,:),dgAOp(:,:,:,:),gAOm(:,:,:),dgAOm(:,:,:,:)
|
||||
double precision,allocatable :: gp(:,:),dgp(:,:,:),gm(:,:),dgm(:,:,:)
|
||||
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: F(nWalk,2,3)
|
||||
|
||||
allocate(rp(nWalk,2,3),rm(nWalk,2,3),r12p(nWalk),r12m(nWalk), &
|
||||
gAOp(nWalk,2,nBas),dgAOp(nWalk,2,3,nBas),gAOm(nWalk,2,nBas),dgAOm(nWalk,2,3,nBas), &
|
||||
gp(nWalk,2),dgp(nWalk,2,3),gm(nWalk,2),dgm(nWalk,2,3))
|
||||
|
||||
do iW=1,nWalk
|
||||
do iEl=1,2
|
||||
do ixyz=1,3
|
||||
|
||||
delta = 1d-6
|
||||
|
||||
rp = r
|
||||
rm = r
|
||||
|
||||
rp(iW,iEl,ixyz) = r(iW,iEl,ixyz) + delta
|
||||
rm(iW,iEl,ixyz) = r(iW,iEl,ixyz) - delta
|
||||
|
||||
call AO_values(.false.,nBas,nShell,nWalk,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,rp,gAOp,dgAOp)
|
||||
call AO_values(.false.,nBas,nShell,nWalk,CenterShell,TotAngMomShell,KShell,DShell,ExpShell,rm,gAOm,dgAOm)
|
||||
|
||||
call Density(.false.,nBas,nWalk,P,gAOp,dgAOp,gp,dgp)
|
||||
call Density(.false.,nBas,nWalk,P,gAOm,dgAOm,gm,dgm)
|
||||
|
||||
call rij(nWalk,rp,r12p)
|
||||
call rij(nWalk,rm,r12m)
|
||||
|
||||
wp = gp(iW,1)*gp(iW,2)/r12p(iW)
|
||||
wm = gm(iW,1)*gm(iW,2)/r12m(iW)
|
||||
|
||||
F(iW,iEl,ixyz) = (wp - wm)/(2d0*delta*w(iw))
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! print*,'NF',F
|
||||
|
||||
|
||||
end subroutine NDrift
|
||||
@ -1,67 +0,0 @@
|
||||
subroutine Newton(nWSq,gradient,hessian,cWeight)
|
||||
|
||||
! Calculate the Green functions
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nWSq
|
||||
double precision,intent(in) :: gradient(nWSq),hessian(nWSq,nWSq)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: info
|
||||
integer,allocatable :: ipiv(:)
|
||||
double precision,allocatable :: scr(:),eigval(:),eigvec(:,:)
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(inout):: cWeight(nWSq)
|
||||
|
||||
! Memory allocation
|
||||
|
||||
allocate(ipiv(nWSq),scr(3*nWsq),eigval(nWSq),eigvec(nWSq,nWSq))
|
||||
|
||||
! Compute eigenvectors and eigenvalues
|
||||
|
||||
eigvec = hessian
|
||||
call dsyev('V','U',nWSq,eigvec,nWSq,eigval,scr,3*nWSq,info)
|
||||
|
||||
if(info /= 0)then
|
||||
write(*,*) ' Problem with dsyev!'
|
||||
stop
|
||||
endif
|
||||
|
||||
write(*,*)
|
||||
write(*,*) 'Eigenvalues of hessian'
|
||||
call matout(nWSq,1,eigval)
|
||||
write(*,*)
|
||||
! write(*,*) 'Eigenvectors of hessian'
|
||||
! call matout(nWSq,1,eigval)
|
||||
! write(*,*)
|
||||
|
||||
! Compute inverse of the hessian
|
||||
|
||||
call dgetrf(nWSq,nWSq,hessian,nWSq,ipiv,info)
|
||||
|
||||
if(info /= 0) then
|
||||
write(*,*) ' Problem in dgetrf!'
|
||||
stop
|
||||
endif
|
||||
|
||||
call dgetri(nWSq,hessian,nWSq,ipiv,scr,nWSq,info)
|
||||
|
||||
if(info /= 0) then
|
||||
write(*,*) ' Problem in dgetri!'
|
||||
stop
|
||||
endif
|
||||
|
||||
print*,'inverse hessian'
|
||||
call matout(nWSq,nWSq,hessian)
|
||||
|
||||
! Compute new coefficients
|
||||
|
||||
cWeight = cWeight - matmul(hessian,gradient)
|
||||
|
||||
end subroutine Newton
|
||||
@ -1,50 +0,0 @@
|
||||
subroutine drift(nWalk,r,r12,g,dg,F)
|
||||
|
||||
! Compute quantum force
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nWalk
|
||||
double precision,intent(in) :: r(nWalk,2,3),r12(nWalk),g(nWalk,2),dg(nWalk,2,3)
|
||||
|
||||
! Local variables
|
||||
|
||||
logical :: smoothDrift
|
||||
double precision :: rij,rijSq,w,wSq,damp
|
||||
integer :: iW
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: F(nWalk,2,3)
|
||||
|
||||
! Compute
|
||||
|
||||
smoothDrift = .false.
|
||||
w = 0.1d0
|
||||
wSq = w*w
|
||||
|
||||
do iW=1,nWalk
|
||||
|
||||
rij = r12(iW)
|
||||
rijSq = rij*rij
|
||||
|
||||
F(iW,1,1:3) = dg(iW,1,1:3)/g(iW,1)
|
||||
F(iW,2,1:3) = dg(iW,2,1:3)/g(iW,2)
|
||||
|
||||
if(smoothDrift) then
|
||||
damp = 1d0 + 2d0*w/sqrt(pi)*rij*exp(-wSq*rijSq)/erfc(w*rij)
|
||||
else
|
||||
damp = 1d0
|
||||
endif
|
||||
|
||||
F(iW,1,1:3) = F(iW,1,1:3) - damp*(r(iW,2,1:3) - r(iW,1,1:3))/rijSq
|
||||
F(iW,2,1:3) = F(iW,2,1:3) - damp*(r(iW,2,1:3) - r(iW,1,1:3))/rijSq
|
||||
|
||||
enddo
|
||||
|
||||
! print*,' F',F
|
||||
|
||||
end subroutine drift
|
||||
@ -1,30 +0,0 @@
|
||||
subroutine generate_shell(atot,nShellFunction,ShellFunction)
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: atot,nShellFunction
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: ax,ay,az,ia
|
||||
|
||||
! Output variables
|
||||
|
||||
integer,intent(out) :: ShellFunction(nShellFunction,3)
|
||||
|
||||
ia = 0
|
||||
do ax=atot,0,-1
|
||||
do az=0,atot
|
||||
ay = atot - ax - az
|
||||
if(ay >= 0) then
|
||||
ia = ia + 1
|
||||
ShellFunction(ia,1) = ax
|
||||
ShellFunction(ia,2) = ay
|
||||
ShellFunction(ia,3) = az
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
end subroutine generate_shell
|
||||
@ -1,25 +0,0 @@
|
||||
subroutine initialize_random_generator(iSeed)
|
||||
|
||||
! Initialize random number generator
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: iSeed
|
||||
|
||||
! Local variables
|
||||
|
||||
integer,allocatable :: Seed(:)
|
||||
integer :: nSeed
|
||||
|
||||
call random_seed(size = nSeed)
|
||||
allocate(Seed(nSeed))
|
||||
call random_seed(get=Seed)
|
||||
if(iSeed /= 0) then
|
||||
Seed = 0
|
||||
Seed(1) = iSeed
|
||||
endif
|
||||
call random_seed(put=Seed)
|
||||
|
||||
end subroutine initialize_random_generator
|
||||
@ -1,53 +0,0 @@
|
||||
subroutine norm_trial(nBas,nO,c,P,Norm,NormSq)
|
||||
|
||||
! Initialize weight function
|
||||
|
||||
implicit none
|
||||
include 'parameters.h'
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nBas,nO
|
||||
double precision,intent(inout):: c(nBas,nO),P(nBas,nBas)
|
||||
|
||||
! Local variables
|
||||
|
||||
double precision,allocatable :: S(:,:),T(:,:),V(:,:),Hc(:,:),G(:,:,:,:)
|
||||
|
||||
integer :: mu,nu,la,si
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(inout):: Norm,NormSq
|
||||
|
||||
! Memory allocation for one- and two-electron integrals
|
||||
|
||||
allocate(S(nBas,nBas),T(nBas,nBas),V(nBas,nBas),Hc(nBas,nBas),G(nBas,nBas,nBas,nBas))
|
||||
|
||||
! Read integrals
|
||||
|
||||
call read_integrals(nBas,S,T,V,Hc,G)
|
||||
|
||||
! Compute normalization factor
|
||||
|
||||
P = 2d0*matmul(c,transpose(c))
|
||||
|
||||
Norm = 0d0
|
||||
do mu=1,nBas
|
||||
do nu=1,nBas
|
||||
do la=1,nBas
|
||||
do si=1,nBas
|
||||
Norm = Norm + P(mu,nu)*P(la,si)*G(mu,la,nu,si)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
Norm = Norm*Norm
|
||||
NormSq = Norm*Norm
|
||||
|
||||
write(*,*)
|
||||
write(*,*) 'Normalization of trial wave function: ',Norm
|
||||
write(*,*)
|
||||
|
||||
end subroutine norm_trial
|
||||
@ -1,28 +0,0 @@
|
||||
subroutine optimize_timestep(nWalk,iMC,Acc,dt)
|
||||
|
||||
! Optimize dt to get 50% of accepted moves
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nWalk,iMC
|
||||
double precision,intent(inout):: Acc,dt
|
||||
|
||||
! Local variables
|
||||
|
||||
double precision :: TotAcc,Current_Acc,Target_Acc,delta
|
||||
|
||||
TotAcc = Acc/dble(nWalk)
|
||||
Current_Acc = 100d0*TotAcc/dble(iMC)
|
||||
|
||||
Target_Acc = 50.0d0
|
||||
|
||||
delta = dt*abs(Target_Acc - Current_Acc)/100.d0
|
||||
if(Current_Acc > Target_Acc + 0.5d0)then
|
||||
dt = dt + delta
|
||||
elseif(Current_Acc < Target_Acc - 0.5d0)then
|
||||
dt = dt - delta
|
||||
endif
|
||||
|
||||
end subroutine optimize_timestep
|
||||
@ -1,41 +0,0 @@
|
||||
subroutine transition_probability(nWalk,dt,D,r,rp,F,Fp,T,Tp)
|
||||
|
||||
! Compute transition probability
|
||||
|
||||
implicit none
|
||||
|
||||
! Input variables
|
||||
|
||||
integer,intent(in) :: nWalk
|
||||
double precision,intent(in) :: dt,D
|
||||
double precision,intent(in) :: r(nWalk,1:2,1:3), F(nWalk,1:2,1:3)
|
||||
double precision,intent(in) :: rp(nWalk,1:2,1:3),Fp(nWalk,1:2,1:3)
|
||||
|
||||
! Local variables
|
||||
|
||||
integer :: iW,iEl,ixyz
|
||||
|
||||
! Output variables
|
||||
|
||||
double precision,intent(out) :: T(nWalk),Tp(nWalk)
|
||||
|
||||
! Initialize
|
||||
|
||||
T = 0d0
|
||||
Tp = 0d0
|
||||
|
||||
! Compute
|
||||
|
||||
do iW=1,nWalk
|
||||
do iEl=1,2
|
||||
do ixyz=1,3
|
||||
T(iW) = T(iW) + (rp(iW,iEl,ixyz) - r(iW,iEl,ixyz) - D*dt*F(iW,iEl,ixyz))**2
|
||||
Tp(iW) = Tp(iW) + (r(iW,iEl,ixyz) - rp(iW,iEl,ixyz) - D*dt*Fp(iW,iEl,ixyz))**2
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
T(:) = exp(-0.25d0*T(:)/(D*dt))
|
||||
Tp(:) = exp(-0.25d0*Tp(:)/(D*dt))
|
||||
|
||||
end subroutine transition_probability
|
||||
Loading…
Reference in New Issue
Block a user