2015-04-03 14:12:51 +02:00
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!!
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!! Computation of Vps, matrix element of the
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!! pseudo-potential centered at point C
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!! Vps= < Phi_A | Vloc(C) + Vpp(C) | Phi_B>
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!! Phi_M (M=A,B) Cartesian gaussian orbital centered at point M :
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!! Phi_M = (x-M_x)**n^M_x *(y-M_y)**n^M_y *(z-M_z)**n^M_z exp(-g_M rM**2)
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!! with rM**2=(x-M_x)**2 + (y-M_y)**2 + (z-M_z)**2
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!!
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!!** Vloc(C)= \sum_{k=1}^klocmax v_k rC**n_k exp(-dz_k rC**2)
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!!
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!!** Vpp(C)= \sum_{l=0}^lmax v_l(rC) \sum_{m=-l}^{m=l} |Y_lm> <Y_lm|
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!!
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!! v_l(rC) = \sum_{k=1}^kmax v_kl rC**n_kl exp(-dz_kl rC**2)
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!!
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!! Y_lm : real spherical harmonics:
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!! Y_00 = sqrt(1/4pi)
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!! Y_11 = sqrt(3/4pi) xchap
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!! Y_10 = sqrt(3/4pi) ychap
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!! Y_1-1 = sqrt(3/4pi) zchap
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!! Y_22 = sqrt(15/16pi) (xchap**2-ychap**2)
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!! Y_21 = sqrt(15/4pi) xchap*zchap
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!! Y_20 = sqrt(15/16pi)(-xchap**2-ychap**2+ 2 zchap**2)
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!! Y_2-1 = sqrt(15/4pi) ychap*zchap
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!! Y_2-2 = sqrt(15/4pi) xchap*ychap
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!! etc.
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!! xchap=x/r ychap=y/r zchap=z/r
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!!
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!! Routine computing <Phi_A|Vpp(C)|Phi_B> :
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!! function Vpseudo(lmax,kmax,v_kl,n_kl,dz_kl,a,n_a,g_a,b,n_b,g_b,c)
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!! lmax of formula above
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!! kmax of formula above
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!! v_kl = array v_kl(kmax_max,0:lmax_max)
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!! n_kl = array n_kl(kmax_max,0:lmax_max)
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!! dz_kl = array dz_kl(kmax_max,0:lmax_max)
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!! n_a(1),n_a(2),n_a(3)
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!! a(1),a(2),a(3)
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!! g_a
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!! n_b(1),n_b(2),n_b(3)
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!! b(1),b(2),b(3)
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!! g_b
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!! c(1),c(2),c(3)
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!!
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!! Routine computing <Phi_A|Vloc(C)|Phi_B> :
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!! function Vloc(klocmax,v_k,n_k,dz_k,a,n_a,g_a,b,n_b,g_b,c)
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!! klocmax of formula above
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!! v_k = array v_k(klocmax_max)
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!! n_k = array n_k(klocmax_max)
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!! dz_k= array dz_k(klocmax_max)
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!! Routine total matrix element <Phi_A|Vloc(C)+Vlpp(C)|Phi_B> :
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!! function Vps(a,n_a,g_a,b,n_b,g_b,c,klocmax,v_k,n_k,dz_k,lmax,kmax,v_kl,n_kl,dz_kl)
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!!
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!! Routines Vps_num, Vpseudo_num, and Vloc_num = brute force numerical
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!! estimations of the same integrals
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program compute_integrals_pseudo
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implicit none
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integer n_a(3),n_b(3),npts
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double precision g_a,g_b,a(3),b(3),c(3)
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double precision Vpseudo,Vpseudo_num,Vloc,Vloc_num
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double precision v3,v4
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double precision vps,vps_num
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! PSEUDOS
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integer nptsgridmax,nptsgrid
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double precision coefs_pseudo,ptsgrid
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double precision rmax
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double precision time_1,time_2,time_3,time_4,time_5
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integer kga,kgb,na1,na2,na3,nb1,nb2,nb3
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CALL RANDOM_SEED()
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nptsgrid=50
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call initpseudos(nptsgrid)
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PROVIDE ezfio_filename
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!
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! | _ _ _. |
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! |_ (_) (_ (_| |
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!
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integer klocmax
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integer, allocatable :: n_k(:)
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double precision, allocatable :: v_k(:), dz_k(:)
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call ezfio_get_pseudo_klocmax(klocmax)
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allocate(n_k(klocmax),v_k(klocmax), dz_k(klocmax))
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call ezfio_get_pseudo_v_k(v_k)
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call ezfio_get_pseudo_n_k(n_k)
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call ezfio_get_pseudo_dz_k(dz_k)
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print*, "klocmax", klocmax
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print*, "n_k_ezfio", n_k
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print*, "v_k_ezfio",v_k
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print*, "dz_k_ezfio", dz_k
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!
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! |\ | _ ._ | _ _ _. |
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! | \| (_) | | | (_) (_ (_| |
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!
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!! Parameters of non local part of pseudo:
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integer :: kmax,lmax
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integer, allocatable :: n_kl(:,:)
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double precision, allocatable :: v_kl(:,:), dz_kl(:,:)
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2015-04-10 09:43:28 +02:00
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call ezfio_get_pseudo_lmaxpo(lmax)
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2015-04-03 14:12:51 +02:00
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call ezfio_get_pseudo_kmax(kmax)
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lmax = lmax - 1
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allocate(n_kl(kmax,0:lmax), v_kl(kmax,0:lmax), dz_kl(kmax,0:lmax))
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call ezfio_get_pseudo_n_kl(n_kl)
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call ezfio_get_pseudo_v_kl(v_kl)
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call ezfio_get_pseudo_dz_kl(dz_kl)
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print*, "lmax",lmax
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print*, "kmax", kmax
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print*,"n_kl_ezfio", n_kl
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print*,"v_kl_ezfio", v_kl
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print*,"dz_kl_ezfio", dz_kl
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! _
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! / _. | _ |
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! \_ (_| | (_ |_| |
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!
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2015-04-07 10:27:22 +02:00
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! write(*,*)'a?'
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! read*,a(1),a(2),a(3)
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2015-04-03 14:12:51 +02:00
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!write(*,*)'b?'
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!read*,b(1),b(2),b(3)
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2015-04-07 10:27:22 +02:00
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! b(1)=-0.1d0
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! b(2)=-0.2d0
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! b(3)=0.3d0
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! !write(*,*)'a?'
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! !read*,c(1),c(2),c(3)
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! c(1)=0.1d0
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! c(2)=0.2d0
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! c(3)=0.3d0
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2015-04-03 14:12:51 +02:00
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2015-04-07 10:27:22 +02:00
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a(1)= 0.d0
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a(2)= 0.d0
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a(3)= 0.d0
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b(1)= 0.d0
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b(2)= 0.d0
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b(3)= 0.d0
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c(1)= 0.d0
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c(2)= 0.d0
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c(3)= 0.d0
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2015-04-03 14:12:51 +02:00
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print*,'ntps? rmax for brute force integration'
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read*,npts,rmax
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do kga=0,5
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g_a=10.d0**kga
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do kgb=0,5
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g_b=10.d0**kgb
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do na1=0,1
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do na2=0,1
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do na3=0,1
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do nb1=0,1
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do nb2=0,1
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do nb3=0,1
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n_a(1)=na1
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n_a(2)=na2
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n_a(3)=na3
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n_b(1)=nb1
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n_b(2)=nb2
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n_b(3)=nb3
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v3=Vps(a,n_a,g_a,b,n_b,g_b,c,klocmax,v_k,n_k,dz_k,lmax,kmax,v_kl,n_kl,dz_kl)
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v4=Vps_num(npts,rmax,a,n_a,g_a,b,n_b,g_b,c,klocmax,v_k,n_k,dz_k,lmax,kmax,v_kl,n_kl,dz_kl)
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print*,'Vps= ',v3,' Vps_num=',v4,' diff=',v4-v3
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write(33,'(3f10.6)')v3,v4,v4-v3
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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enddo
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end
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