## File: rlmrot.f90

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elkcode 5.4.24-2
 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119  ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rlmrot ! !INTERFACE: subroutine rlmrot(p,ang,lmax,ld,d) ! !INPUT/OUTPUT PARAMETERS: ! p : if p=-1 then the rotation matrix is improper (in,integer) ! ang : Euler angles; alpha, beta, gamma (in,real(3)) ! lmax : maximum angular momentum (in,integer) ! ld : leading dimension (in,integer) ! d : real spherical harmonic rotation matrix (out,real(ld,*)) ! !DESCRIPTION: ! Returns the rotation matrix in the basis of real spherical harmonics given ! the three Euler angles, $(\alpha,\beta,\gamma)$, and the parity, $p$, of the ! rotation. The matrix is determined using the formula of V. V. Nechaev, ! [{\it J. Struct. Chem.} {\bf 35}, 115 (1994)], suitably modified for our ! definition of the real spherical harmonics ($m_1>0$, $m_2>0$): ! \begin{align*} ! &\Delta^l_{00}=d^l_{00}, \\ ! &\Delta^l_{m_10}=\sqrt{2}\,(-1)^{m_1}d^l_{0m_1}\cos(m_1\alpha), \\ ! &\Delta^l_{0m_2}=\sqrt{2}\,(-1)^{m_2}d^l_{m_20}\cos(m_2\gamma), \\ ! &\Delta^l_{-m_10}=-\sqrt{2}\,d^l_{0m_1}\sin(m_1\alpha), \\ ! &\Delta^l_{0-m_2}=\sqrt{2}\,d^l_{m_20}\sin(m_2\gamma), \\ ! &\Delta^l_{m_1m_2}=(-1)^{m_1}(-1)^{m_2}\{\cos(m_1\alpha)\cos(m_2\gamma) ! [d_A+d_B]-\sin(m_1\alpha)\sin(m_2\gamma)[d_A-d_B]\}, \\ ! &\Delta^l_{m_1-m_2}=(-1)^{m_1}\{\sin(m_1\alpha)\cos(m_2\gamma) ! [d_A-d_B]+\cos(m_1\alpha)\sin(m_2\gamma)[d_A+d_B]\}, \\ ! &\Delta^l_{-m_1m_2}=-(-1)^{m_2}\{\sin(m_1\alpha)\cos(m_2\gamma) ! [d_A+d_B]+\cos(m_1\alpha)\sin(m_2\gamma)[d_A-d_B]\}, \\ ! &\Delta^l_{-m_1-m_2}=\cos(m_1\alpha)\cos(m_2\gamma) ! [d_A-d_B]-\sin(m_1\alpha)\sin(m_2\gamma)[d_A+d_B], ! \end{align*} ! where $d_A\equiv d^l_{-m_1-m_2}$, $d_B\equiv(-1)^{m_1}d^l_{m_1-m_2}$ and ! $d$ is the rotation matrix about the $y$-axis for complex spherical ! harmonics. See the routines {\tt genrlm}, {\tt roteuler} and {\tt ylmroty}. ! ! !REVISION HISTORY: ! Created December 2008 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: p real(8), intent(in) :: ang(3) integer, intent(in) :: lmax,ld real(8), intent(out) :: d(ld,*) ! local variables integer l,m1,m2,lm,lm0 real(8), parameter :: sqtwo=1.4142135623730950488d0 real(8) s1,s2,t1,t2,t3,t4,t5,t6,t7,t8 ! automatic arrays integer lmi(-lmax:lmax) real(8) ca(lmax),sa(lmax),cg(lmax),sg(lmax) ! automatic arrays real(8) dy(ld,ld) if (lmax.lt.0) then write(*,*) write(*,'("Error(rlmrot): lmax < 0 : ",I8)') lmax write(*,*) stop end if ! generate the complex spherical harmonic rotation matrix about the y-axis call ylmroty(ang(2),lmax,ld,dy) do m1=1,lmax ca(m1)=cos(m1*ang(1)) sa(m1)=sin(m1*ang(1)) cg(m1)=cos(m1*ang(3)) sg(m1)=sin(m1*ang(3)) end do lm=0 do l=0,lmax do m1=-l,l lm=lm+1 lmi(m1)=lm end do lm0=lmi(0) d(lm0,lm0)=dy(lm0,lm0) do m1=1,l s1=1.d0 if (mod(m1,2).ne.0) s1=-1.d0 t1=sqtwo*dy(lm0,lmi(m1)) t2=sqtwo*dy(lmi(m1),lm0) d(lmi(m1),lm0)=s1*t1*ca(m1) d(lm0,lmi(m1))=s1*t2*cg(m1) d(lmi(-m1),lm0)=-t1*sa(m1) d(lm0,lmi(-m1))=t2*sg(m1) do m2=1,l s2=1.d0 if (mod(m2,2).ne.0) s2=-1.d0 t1=ca(m1)*cg(m2) t2=sa(m1)*sg(m2) t3=sa(m1)*cg(m2) t4=ca(m1)*sg(m2) t5=dy(lmi(-m1),lmi(-m2)) t6=s1*dy(lmi(m1),lmi(-m2)) t7=t5+t6 t8=t5-t6 d(lmi(m1),lmi(m2))=s1*s2*(t1*t7-t2*t8) d(lmi(m1),lmi(-m2))=s1*(t3*t8+t4*t7) d(lmi(-m1),lmi(m2))=-s2*(t3*t7+t4*t8) d(lmi(-m1),lmi(-m2))=t1*t8-t2*t7 end do end do if ((p.eq.-1).and.(mod(l,2).ne.0)) then do m1=-l,l do m2=-l,l d(lmi(m1),lmi(m2))=-d(lmi(m1),lmi(m2)) end do end do end if end do return end subroutine !EOC