Dev spher harm

plugins/local/basis_correction/51.basis_c.bats

@@ -37,14 +37,6 @@ function run_sd() {
   eq $energy1 $1 $thresh
 }
 
-@test "O2 CAS" {  
-  qp set_file o2_cas.gms.ezfio
-  qp set_mo_class -c "[1-2]" -a "[3-10]" -d "[11-46]"
-  run -149.72435425 3.e-4 10000
-  qp set_mo_class -c "[1-2]" -a "[3-10]" -v "[11-46]"
-  run_md -0.1160222327 1.e-6 
-}
-
 
 @test "LiF RHF" {  
   qp set_file lif.ezfio 

plugins/local/normal_order_old/NEED

@@ -1 +1 @@
-
+tc_scf

plugins/local/spher_harm/.gitignore

@@ -0,0 +1,59 @@
+IRPF90_temp/
+IRPF90_man/
+build.ninja
+irpf90.make
+ezfio_interface.irp.f
+irpf90_entities
+tags
+Makefile
+ao_basis
+ao_one_e_ints
+ao_two_e_erf_ints
+ao_two_e_ints
+aux_quantities
+becke_numerical_grid
+bitmask
+cis
+cisd
+cipsi
+davidson
+davidson_dressed
+davidson_undressed
+density_for_dft
+determinants
+dft_keywords
+dft_utils_in_r
+dft_utils_one_e
+dft_utils_two_body
+dressing
+dummy
+electrons
+ezfio_files
+fci
+generators_cas
+generators_full
+hartree_fock
+iterations
+kohn_sham
+kohn_sham_rs
+mo_basis
+mo_guess
+mo_one_e_ints
+mo_two_e_erf_ints
+mo_two_e_ints
+mpi
+mrpt_utils
+nuclei
+perturbation
+pseudo
+psiref_cas
+psiref_utils
+scf_utils
+selectors_cassd
+selectors_full
+selectors_utils
+single_ref_method
+slave
+tools
+utils
+zmq

plugins/local/spher_harm/NEED

@@ -0,0 +1 @@
+dft_utils_in_r

plugins/local/spher_harm/README.rst

@@ -0,0 +1,7 @@
+==========
+spher_harm
+==========
+
+Routines for spherical Harmonics evaluation in real space. 
+The main routine is "spher_harm_func_r3(r,l,m,re_ylm, im_ylm)".  
+The test routine is "test_spher_harm" where everything is explained in details. 

plugins/local/spher_harm/assoc_gaus_pol.irp.f

@@ -0,0 +1,50 @@
+double precision function plgndr(l,m,x)
+ integer, intent(in) :: l,m
+ double precision, intent(in) :: x
+ BEGIN_DOC
+ ! associated Legenre polynom P_l,m(x). Used for the Y_lm(theta,phi)
+ ! Taken from https://iate.oac.uncor.edu/~mario/materia/nr/numrec/f6-8.pdf
+ END_DOC
+ integer :: i,ll
+ double precision :: fact,pll,pmm,pmmp1,somx2
+ if(m.lt.0.or.m.gt.l.or.dabs(x).gt.1.d0)then 
+  print*,'bad arguments in plgndr'
+  pause
+ endif
+ pmm=1.d0
+ if(m.gt.0) then
+  somx2=dsqrt((1.d0-x)*(1.d0+x))
+  fact=1.d0
+  do i=1,m
+   pmm=-pmm*fact*somx2
+   fact=fact+2.d0
+  enddo 
+ endif ! m > 0
+ if(l.eq.m) then
+  plgndr=pmm 
+ else
+  pmmp1=x*(2*m+1)*pmm ! Compute P_m+1^m
+   if(l.eq.m+1) then
+    plgndr=pmmp1
+   else ! Compute P_l^m, l> m+1
+    do ll=m+2,l
+     pll=(x*dble(2*ll-1)*pmmp1-dble(ll+m-1)*pmm)/(ll-m)
+     pmm=pmmp1
+     pmmp1=pll
+    enddo
+    plgndr=pll
+   endif ! l.eq.m+1
+ endif ! l.eq.m
+ return
+end
+
+double precision function ortho_assoc_gaus_pol(l1,m1,l2)
+ implicit none
+ integer, intent(in) :: l1,m1,l2
+ double precision :: fact
+ if(l1.ne.l2)then
+  ortho_assoc_gaus_pol= 0.d0
+ else
+  ortho_assoc_gaus_pol = 2.d0*fact(l1+m1) / (dble(2*l1+1)*fact(l1-m1))
+ endif
+end

plugins/local/spher_harm/routines_test.irp.f

@@ -0,0 +1,231 @@
+subroutine test_spher_harm
+ implicit none
+ BEGIN_DOC
+ ! routine to test the generic spherical harmonics routine "spher_harm_func_r3" from R^3 --> C
+ ! 
+ ! We test <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2
+ ! 
+ ! The test is done through the integration on a sphere with the Lebedev grid. 
+ END_DOC
+  include 'constants.include.F'
+ integer :: l1,m1,i,l2,m2,lmax
+ double precision :: r(3),weight,accu_re, accu_im,accu
+ double precision :: re_ylm_1, im_ylm_1,re_ylm_2, im_ylm_2
+ double precision :: theta,phi,r_abs
+ lmax = 5 ! Maximum angular momentum until which we are going to test orthogonality conditions
+ do l1 = 0,lmax
+  do m1 =  -l1 ,l1
+   do l2 = 0,lmax
+    do m2 =  -l2 ,l2
+     accu_re = 0.d0 ! accumulator for the REAL part of <Y_l1,m1|Y_l2,m2>
+     accu_im = 0.d0 ! accumulator for the IMAGINARY part of <Y_l1,m1|Y_l2,m2>
+     accu    = 0.d0 ! accumulator for the weights ==> should be \int dOmega == 4 pi
+     ! <l1,m1|l2,m2> = \int dOmega Y_l1,m1^* Y_l2,m2 
+     !               \approx \sum_i W_i Y_l1,m1^*(r_i) Y_l2,m2(r_i) WITH r_i being on the spher of radius 1 
+     do i = 1, n_points_integration_angular 
+      r(1:3) = angular_quadrature_points(i,1:3) ! ith Lebedev point (x,y,z) on the sphere of radius 1 
+      weight = weights_angular_points(i)        ! associated Lebdev weight not necessarily positive 
+
+!!!!!!!!!!! Test of the Cartesian --> Spherical coordinates  
+      ! theta MUST belong to [0,pi] and phi to [0,2pi]
+      ! gets the cartesian to spherical change of coordinates 
+      call cartesian_to_spherical(r,theta,phi,r_abs)
+      if(theta.gt.pi.or.theta.lt.0.d0)then
+       print*,'pb with theta, it should be in [0,pi]',theta
+       print*,r
+      endif
+      if(phi.gt.2.d0*pi.or.phi.lt.0.d0)then
+       print*,'pb with phi, it should be in [0,2 pi]',phi/pi
+       print*,r
+      endif
+
+!!!!!!!!!!! Routines returning the Spherical harmonics on the grid point 
+      call spher_harm_func_r3(r,l1,m1,re_ylm_1, im_ylm_1)
+      call spher_harm_func_r3(r,l2,m2,re_ylm_2, im_ylm_2)
+
+!!!!!!!!!!! Integration of Y_l1,m1^*(r) Y_l2,m2(r)
+     !               = \int dOmega (re_ylm_1 -i im_ylm_1) * (re_ylm_2 +i im_ylm_2)
+     !               = \int dOmega (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2) +i (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
+      accu_re += weight * (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2)
+      accu_im += weight * (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
+      accu += weight
+     enddo
+     ! Test that the sum of the weights is 4 pi
+     if(dabs(accu - dfour_pi).gt.1.d-6)then
+      print*,'Problem !! The sum of the Lebedev weight is not 4 pi ..'
+      print*,accu
+      stop
+     endif
+     ! Test for the delta l1,l2 and delta m1,m2
+     !
+     ! Test for the off-diagonal part of the Kronecker delta 
+     if(l1.ne.l2.or.m1.ne.m2)then
+      if(dabs(accu_re).gt.1.d-6.or.dabs(accu_im).gt.1.d-6)then
+       print*,'pb OFF DIAG !!!!! '
+       print*,'l1,m1,l2,m2',l1,m1,l2,m2
+       print*,'accu_re = ',accu_re
+       print*,'accu_im = ',accu_im
+      endif
+     endif
+     ! Test for the diagonal part of the Kronecker delta 
+     if(l1==l2.and.m1==m2)then
+      if(dabs(accu_re-1.d0).gt.1.d-5.or.dabs(accu_im).gt.1.d-6)then
+       print*,'pb DIAG !!!!! '
+       print*,'l1,m1,l2,m2',l1,m1,l2,m2
+       print*,'accu_re = ',accu_re
+       print*,'accu_im = ',accu_im
+      endif
+     endif
+    enddo
+   enddo
+  enddo
+ enddo
+end
+
+subroutine test_cart
+ implicit none
+ BEGIN_DOC
+ ! test for the cartesian --> spherical change of coordinates 
+ !
+ ! test the routine "cartesian_to_spherical" such that the polar angle theta ranges in [0,pi]
+ !
+ ! and the asymuthal angle phi ranges in [0,2pi]
+ END_DOC
+ include 'constants.include.F'
+ double precision :: r(3),theta,phi,r_abs 
+ print*,''
+ r = 0.d0
+ r(1) = 1.d0
+ r(2) = 1.d0
+ call cartesian_to_spherical(r,theta,phi,r_abs)
+ print*,r
+ print*,phi/pi
+ print*,''
+ r = 0.d0
+ r(1) =-1.d0
+ r(2) = 1.d0
+ call cartesian_to_spherical(r,theta,phi,r_abs)
+ print*,r
+ print*,phi/pi
+ print*,''
+ r = 0.d0
+ r(1) =-1.d0
+ r(2) =-1.d0
+ call cartesian_to_spherical(r,theta,phi,r_abs)
+ print*,r
+ print*,phi/pi
+ print*,''
+ r = 0.d0
+ r(1) = 1.d0
+ r(2) =-1.d0
+ call cartesian_to_spherical(r,theta,phi,r_abs)
+ print*,r
+ print*,phi/pi
+end
+
+
+subroutine test_brutal_spheric
+ implicit none
+  include 'constants.include.F'
+ BEGIN_DOC
+ ! Test for the <Y_l1,m1|Y_l2,m2> = delta_m1,m2 delta_l1,l2 using the following two dimentional integration 
+ ! 
+ !   \int_0^2pi d Phi \int_-1^+1 d(cos(Theta)) Y_l1,m1^*(Theta,Phi) Y_l2,m2(Theta,Phi)
+ !
+ !=  \int_0^2pi d Phi \int_0^pi dTheta sin(Theta)  Y_l1,m1^*(Theta,Phi) Y_l2,m2(Theta,Phi) 
+ !
+ ! Allows to test for the general functions "spher_harm_func_m_pos" with "spher_harm_func_expl"
+ END_DOC
+ integer :: itheta, iphi,ntheta,nphi
+ double precision :: theta_min, theta_max, dtheta,theta
+ double precision :: phi_min, phi_max, dphi,phi
+ double precision :: accu_re, accu_im,weight 
+ double precision :: re_ylm_1, im_ylm_1 ,re_ylm_2, im_ylm_2,accu
+ integer :: l1,m1,i,l2,m2,lmax
+ phi_min = 0.d0
+ phi_max = 2.D0 * pi
+ theta_min = 0.d0
+ theta_max = 1.D0 * pi
+ ntheta = 1000
+ nphi = 1000
+ dphi = (phi_max - phi_min)/dble(nphi)
+ dtheta = (theta_max - theta_min)/dble(ntheta)
+
+ lmax = 2
+ do l1 = 0,lmax
+  do m1 =  0 ,l1
+   do l2 = 0,lmax
+    do m2 =  0 ,l2
+     accu_re = 0.d0
+     accu_im = 0.d0
+     accu  = 0.d0
+     theta = theta_min
+     do itheta = 1, ntheta
+      phi = phi_min
+      do iphi = 1, nphi
+!      call spher_harm_func_expl(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
+!      call spher_harm_func_expl(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
+       call spher_harm_func_m_pos(l1,m1,theta,phi,re_ylm_1, im_ylm_1)
+       call spher_harm_func_m_pos(l2,m2,theta,phi,re_ylm_2, im_ylm_2)
+       weight = dtheta * dphi * dsin(theta) 
+       accu_re += weight * (re_ylm_1*re_ylm_2 + im_ylm_1*im_ylm_2)
+       accu_im += weight * (im_ylm_2*re_ylm_1 - im_ylm_1*re_ylm_2)
+       accu += weight
+       phi += dphi
+      enddo
+      theta += dtheta
+     enddo
+     print*,'l1,m1,l2,m2',l1,m1,l2,m2
+     print*,'accu_re = ',accu_re
+     print*,'accu_im = ',accu_im
+     print*,'accu    = ',accu
+     if(l1.ne.l2.or.m1.ne.m2)then
+      if(dabs(accu_re).gt.1.d-6.or.dabs(accu_im).gt.1.d-6)then
+       print*,'pb OFF DIAG !!!!! '
+      endif
+     endif
+     if(l1==l2.and.m1==m2)then
+      if(dabs(accu_re-1.d0).gt.1.d-5.or.dabs(accu_im).gt.1.d-6)then
+       print*,'pb DIAG !!!!! '
+      endif
+     endif
+    enddo
+   enddo
+  enddo
+ enddo
+
+
+end
+
+subroutine test_assoc_leg_pol
+  implicit none
+  BEGIN_DOC
+! Test for the associated Legendre Polynoms. The test is done through the orthogonality condition. 
+  END_DOC
+  print *, 'Hello world'
+ integer :: l1,m1,ngrid,i,l2,m2
+ l1 = 0
+ m1 = 0
+ l2 = 2
+ m2 = 0
+ double precision :: x, dx,xmax,accu,xmin
+ double precision :: plgndr,func_1,func_2,ortho_assoc_gaus_pol
+ ngrid = 100000
+ xmax = 1.d0
+ xmin = -1.d0
+ dx = (xmax-xmin)/dble(ngrid)
+ do l2 = 0,10
+  x = xmin
+  accu = 0.d0
+  do i = 1, ngrid
+   func_1 = plgndr(l1,m1,x)
+   func_2 = plgndr(l2,m2,x)
+   write(33,*)x, func_1,func_2
+   accu += func_1 * func_2 * dx
+   x += dx
+  enddo
+  print*,'l2 = ',l2
+  print*,'accu = ',accu
+  print*,ortho_assoc_gaus_pol(l1,m1,l2)
+ enddo
+end

plugins/local/spher_harm/spher_harm.irp.f

@@ -0,0 +1,7 @@
+program spher_harm
+ implicit none
+! call test_spher_harm
+! call test_cart
+ call test_brutal_spheric
+end
+