CCL:G: CASSCF problems

 Sent to CCL by: =?Windows-1252?Q?J=FCrgen_Gr=E4fenstein?= [jurgen{:}chem.gu.se]
 Dear Thomas,
 I suppose you mix up NO with the situation in O_2. In O_2, you have two
 electrons in the (antibonding) pi orbitals. Here, DFT/HF are unable to properly
 describe
 the singlet states. None of the configurations (pi_x_alpha+pi_x_beta,
 pi_y_alpha+pi_y_beta, pi_x_alpha+pi_y_beta, pi_y_alpha+pi_x_beta ) are
 eigenfunctions to the
 L_z operator. Rather, the mentioned configurations have to be combined to form
 (i) one component of the ^3\Sigma_g^– multiplet (the other two being
 pi_x_alpha+pi_y_alpha and pi_x_beta+pi_y_beta), (ii) a ^1\Sigma_g^+ state, and
 (ii) a pair of ^1\Delta_g states.
 (Sorry for the inconsistent notation, I hope it works!)
 In NO, on the contrary, you have just one electron in the antibonding pi
 orbitals. This electron may sit in either pi_x or pi_y (or "tilted").
 The many-particle state of NO is thus degenerate
 (^2\Pi) not only with respect to spin but also with respect to the L_z value (+1
 or -1, alternatively Pi_x or Pi_y). Any wavefunction for that state will break
 rotational symmetry around the axis of the molecule. Thus, in this case the
 essence of the HF/DFT MO picture survives the inclusion of non-dynamical
 correlations. To restore rotational symmetry around the molecular axis, you have
 to merge Pi_x and Pi_y states into a mixed state, which needs to be described by
 a many-electron density matrix rather than a wavefunction. It is this mied state
 that is descried by FON-DFT or state-averaged CASSCF.
 As for the optimization, Gaussian should provide a full 2nd-order algorithm.
 There may be no keyword to invoke it, so you need to specify an option. In G03,
 it was IOp(5/17=100). Please be advised, however, that I have little to no
 experience with tricky CASSCF optimizations.
 Best regards,
 Jürgen
 Sent to CCL by: Thomas Exner [thomas.exner*|*uni-konstanz.de]
 Dear Jürgen:
 Thank you very much for pointing me to the FON-DFT approach. I will
 definitely look into it. But I still think that standard CASSCF should
 be able to get it right. Perhaps I make a complete fool out of me,
 anyway: In an MO picture, there are the two degenerated states (pi_x and
 pi_y) and HF and DFT, which take no non-dynamic correlation into
 account, should convert to one of these. But the NO molecule should show
 a symmetric electron distribution, which shows, in my opinion, that the
 MO scheme is misleading. Fractional occupation numbers help here, since
 one can put half an electron in each of the two degenerated pi orbitals.
 But is that not exactly what CASSCF is meant for. By combining multiple
 electron configurations, the calculation should be able (in a very
 simplified way to demonstrate my point) to take the two configuration
 with the unpaired electron in the pi_x orbital and in the pi_y orbital,
 respectively, with equal contribution. This would then result in an
 electron occupation of 0.5 in both orbitals, exactly what I expect. Any
 comments on that or a reason, why I am wrong?
 And, really no suggestions for my second question?
 "Additionally, I have a larger system for which I also perform casscf
 calculations. Ground state simulations and also the first excited state
 using the ground state geometry are fine. Energy optimization in the
 excited state also starts ok but after some steps the calculation does
 not converge anymore. Use of "use=l506" as proposed in the g09 manual
 did not help. Also no luck with increasing the maxcycle or starting with
 an other conformation. Is there anything else I can try? Perhaps there
 are some options for the optimizer that he does not jump into the bad
 region with the convergence problems. Unfortunately, the "sleazy" and
 the "qc" keyword for scf cannot be used with casscf
 optimization."
 Thanks.
 Thomas