*From*: frisch #*at*# gaussian.com (Mike Frisch)*Subject*: Re: CCL:G:How to keep a particular state*Date*: Thu, 16 Nov 1995 16:47:01 -0500 (EST)

There have been several questions about SCF and different electronic states, and enough mis-information has been posted that a coherent reply is needed. Several different issues have been mixed together in the responses: 1. Getting Gaussian to find an SCF solution of a particular symmetry. 2. Whether SCF always converges to the ground state. 3. Whether an SCF solution different from the ground state (lowest) solution but of the same symmetry is phycially meaning ful. 4. Whether one always wants the ground state in all calculations, or all calculations involving a reaction. The original question was about either 1 or 3 (it was open to either interpretation). First of all, an SCF can converge to a minimum or a saddle point in the space of possible wavefunctions. The nature of the stationary point found can be testing by finding if the orbital rotation Hessian has any negative eigenvalues (Stable keyword in G94, or Stable=Opt to move downhill to a local minimum). Once a minimum is found, it is not guaranteed to be the global minimum, although it usually is in practice. (In fact, it takes some effort to produce an example of multiple local minima, and this usually involves stretching multiple bonds.) There is a rather useless theorem that if pure SCF (without DIIS or any other extrapolation) converges, then the resulting wavefunction is a local minimum. In practice, pure SCF is so slow and unreliable that everyone uses some extrapolation method. This greatly reduces the number of SCF iterations required and greatly increases the likelihood of finding a solution but does create the possibility of finding a saddle point instead of a minimum. The theorem has led some people to the false assumption that if the SCF converges, even with normal extrapolation proceedures, then it must be stable. In practice, the stability should be tested if there is any doubt or uncertainty about the solution -- this includes any case in which significant convergence difficulties are encountered. If a solution of the SCF equations which has a different symmetry than the ground state is found, then the variational principle applies and the energy of this state is an upper bound on the energy of the lowest excited state of its symmetry. If the SCF is started with an initial guess of a different symmetry than the ground state and is constrained to consider wavefunctions of only this symmetry, then such a solution can be found. This is typically done by keeping the number of occupied orbitals of each symmetry type fixed. The route command for this in Gaussian 94 is SCF=Symm. A solution of the standard SCF equations which is of the same symmetry as the ground state only provides an upper bound on the ground state energy. A solution with the same symmetry as the ground state which is not the lowest solution is an arbitrary mixture of the ground state and excited states of the same symmetry. It does not provide an upper bound on any energy except the ground state, and is not a good approximation to the the wavefunction for any excited state, since it has an unknown amount of ground state mixed in. These general excited states must be studied by a method which enforces orthogonality to the ground state, such as CIS or CASSCF. While typical reactions occur entirely on the ground state potential energy surface, as one poster noted, there are many cases of surface crossings. These are an important feature of photochemical reactions. The usual case of ground state reactions can be reliably studied in Gaussian by using Stable=Opt to ensure that the wavefunctions used at each structure are minima in wavefunction space. For details on studying conical intersections and related photochemistry, see the appropriate references to Mike Robb's work in the Gaussian manual. Mike Frisch frisch #*at*# lorentzian.com