Simple Hartree-Fock example
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Description: By Paul Stevenson, in Fortran 90.
! Simple nuclear Hartree-Fock program. 2003. ! http://www.ph.surrey.ac.uk/~phs3ps/simple-hf.html program simplehf implicit none integer :: i, j integer, parameter :: maxiter = 1000 integer, parameter :: npoints = 40 real, parameter :: dr = 0.2 real, parameter :: fourpi = 12.56637061432 real, parameter :: hbrm = 41.437 real, parameter :: hob = 1.4 ! damping parameter real, parameter :: xdamp = 0.0001 ! storage of single particle state real, dimension(npoints) :: wavefunction ! density real, dimension(npoints) :: density ! HF potential real, parameter :: t0 = -1090.0, t3 = 17488.0 real, dimension(npoints) :: potential ! a vector with the r-grid points real, dimension(npoints) :: r_grid ! some workspace real, dimension(npoints) :: scr1 ! single particle potential and kinetic energies real :: spe, ke, speold ! Initialize r-grid r_grid = (/ (i*dr,i=0,npoints-1) /) ! Initialize the wave function with a gaussian wavefunction = (r_grid/hob) * exp(-(r_grid/hob)**2/2) ! normalize wavefunction wavefunction = wavefunction / sqrt(dr*sum(wavefunction**2)) ! Start HF iteration here speold=HUGE(1.0) do i=1,maxiter ! calculate density density(2:npoints) = 4*( wavefunction(2:) / r_grid(2:) )**2 / fourpi ! special at the origin based on L'H ital's rule density(1) = 4*( (4*wavefunction(2)/3-wavefunction(3)/6) /dr)**2/fourpi potential = 3*t0/4 * density + 3*t3/16 * density**2 ! act with kinetic energy operator on wavefunction using 3-pt. formula scr1(1) = hbrm*wavefunction(1)/dr**2 do j=2,npoints-1 scr1(j) = -hbrm/2*(wavefunction(j-1)-2*wavefunction(j)+ & wavefunction(j+1))/dr**2 end do scr1(npoints) = -hbrm/2*(wavefunction(npoints-1)- & wavefunction(npoints))/dr**2 ke = dr * sum(scr1*wavefunction) scr1 = scr1 + potential*wavefunction spe = dr * sum(scr1*wavefunction) ! print out some information every 20 iterations if(mod(i,20)==0) write(6,*) "It,ke,spe,conv=",i,ke,spe,abs(spe-speold) speold=spe ! update wavefunction wavefunction = wavefunction - xdamp * (scr1-spe*wavefunction) wavefunction = wave
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