Response output

While the calculations are being done, the program prints the progress of the optimization process:

• The ``scaling input'' prints the number by which the right-hand-side of Eq. (242) is multiplied in order to deal with reasonable numbers during the optimization. The number is determined through the condition

  
  

  $$\vert\vert\;H^{(1)}\vert\varphi_{k}^{(0)}\rangle \;\vert\vert_2 = 1.$$ (248)

  
  

  When leaving the optimization routine, the inverse scaling is applied to the $\vert\varphi_{k}^{(1)}\rangle$ , of course.

• The standard output shows (A) the maximum gradient of the second order energy with respect to the first order perturbation wavefunction, (B) the norm of that gradient, (C) the second order energy, (D) its difference with respect to the last value, and finally (E) the CPU time needed for one step. The last value decreases by somewhat after the number of steps determined by the CG-ANALYTIC keyword, because the analytic line search is no longer performed, as discussed above.

• A line full of tildes ( $\tilde{ }$ ) indicates that the energy has increased. In that case, the conjugate direction is erased and the conjugate gradient routine is restarted. Also the time step is calculated again using the analytic quadratic line search formula.

• The warning ``line search instable'' indicates that the length which has been calculated using the analytic quadratic line search approximation (Numerical Recipes Eq. 10.6.4) has given a numerical values larger than 3. This does not happen in normal cases, and it can yield to program crashes due to floating point overflows ($\mapsto$ NaN, not a number). Thus, a safe value, 1, is used instead.

• The warning ``gradient norm increased by more than 200%'' indicates that the quadratic approximation is not valid in the momentary position of the optimization. If it was, the gradient (of the energy with respect to the first order perturbation wavefunctions) would only decrease and finally reach zero. If this situation occurs, the conjugate direction is erased and the conjugate gradient algorithm is restarted.