def dihedros(A_1,A_2,A_3,A_4,qt_1):
    xba = A_2.x - A_1.x ;  xca = A_3.x - A_1.x
    yba = A_2.y - A_1.y ;  yca = A_3.y - A_1.y
    zba = A_2.z - A_1.z ;  zca = A_3.z - A_1.z
    xcb = A_3.x - A_2.x ;  xdb = A_4.x - A_2.x
    ycb = A_3.y - A_2.y ;  ydb = A_4.y - A_2.y
    zcb = A_3.z - A_2.z ;  zdb = A_4.z - A_2.z
    nx1=(yba*zca)-(yca*zba)
    ny1=(xca*zba)-(xba*zca)
    nz1=(xba*yca)-(xca*yba)
    nx2=(ycb*zdb)-(ydb*zcb)
    ny2=(xdb*zcb)-(xcb*zdb)
    nz2=(xcb*ydb)-(xdb*ycb)
    pdot = (nx1*nx2)+(ny1*ny2)+(nz1*nz2)
    w1 = sqrt((nx1*nx1)+(ny1*ny1)+(nz1*nz1))
    w2 = sqrt((nx2*nx2)+(ny2*ny2)+(nz2*nz2))
    signo = (nx2*xba)+(ny2*yba)+(nz2*zba)
    u = pdot/(w1*w2)
    if abs(u) >= 1.0:
        u=(1.-1.e-20)*(u/abs(u))
    if signo >= 0.:
        dieh = acos(u)
        qa = dieh - 2*pi
    if signo < 0.:
        dieh = -acos(u)
        qa = dieh + 2*pi

    wa = dieh - qt_1; wb = qa - qt_1
    if abs(wa) <= abs(wb):
        ang_dih = dieh
    else:
        ang_dih = qa

    return ang_dih