Please advise me about the stability test for Gaussian/DFT calculation.
It is common that in reported papers, frequency check is mentioned but to much lesser extend is stability test.
I test for most of my compounds (Ru(bpy)3 2+ singlet/first triplet optimized structures, stable keyword, same functional/basis set) and the test always results in "stable".
So how important is the test in DFT calculation?
Is that quite often we got a instable wavafunction resulted from an optimization?
If unstable is found, then run a job stable=opt, then continue working (lets say SP, TD-DFT, POP...) with the newly generated chk file (same geometry, new wavefunction), right?
Thank you!
Actually, stability check is just CIS procedure for the HF reference or TDDFT (RPA) for the KS wavefunction. The instability appears when some eigenvalue of the CIS(RPA) matrix is lower than eigenvalue of the reference state. Assuming the reference as zero, negative eigenvalue indicates instability. Think about these eigenvalues as squares of the vibrational frequencies and you will find pretty good analogy with geometry optimization check: to be sure that geometry is minimum you should not have imaginary frequencies. Of course, the hessian matrix calculation should be done in the same level of theory as geometry optimization. The same is true for wavefunction stability check. Therefore, at your level of theory this particular triplet is lowest only if its pass stability check.
Since stability check is actually cumbersome procedure, you may be interested in method of finding true ground state from the beginning. To achieve that, your initial guess should be BAD, that mean guess=core or something. The best option is completely randomized wavefunction, to be sure that initial guess has nonzero overlap with true ground state. Good guesses are good only if they overlap with true ground state, but you cannot be sure in advance that Gaussian offer you that kind of initial guess. By default, Gaussian optimized for speed of the SCF procedure, that means initial guess generated requires only 10-20 steps to converge. Guess=mix makes guess worse, but allows one to converge into broken symmetry biradical solution. On the other side, the bad guess results in bad SCF convergence.
Happily, there is solution. Instead of the ordinary DIIS (commutator-based DIIS) convergence accelerator, which suffers from the bad guesses, but converge fast, there is EDIIS (energy-based DIIS) which has guaranteed convergence, but slow. Since Gaussian 09 EDIIS+CDIIS combination is used. You may tune this combination from speed(default) to guaranteed ground state convergence. In the difficult cases I prefer the following combination: Guess=Core or Guess=mix together with iop(5/22=6032) scf=(MaxCycles=500). This turns on EDIIS from the beginning and switches to CDIIS only if commutator is pretty small (10**-6) to be sure that we achieve ground state.
i hope this information will be helpful.
Wavefunction stability test is important in following cases: 1) when some point group symmetry is used, initial guess sometimes do wrong suggestion about ground state symmetry irreducible representation, stability check can find true ground state irrep 2) when biradical electronic structure is appeared, for example, in transition state search. I think the second case is of great importance, since most reaction mechanisms are thought to be based on a some closed-shell electron-pair movement, but detailed researches using CIDNP (Chemically Induced Dynamic Nuclear Polarization) spectroscopy revealed possibilities for the radical mechanisms in case where it was not evident from the beginning.
Consider also the problem os singlet-triplet instability, e.g. in long poliacenes, in which from a certain molecular size the triplet state becomes the ground state. When one claculates the singlet state as the ground state, its wavefunction becomes unstable with respect to the triplet state one. The stability analysis should reflect the order change.
Also, when you try to compute the lowest triplet state in case it is indeed the excited state, you may (instead of using the TDDFT approach) set the initial orbital occupation and compute the triplet stae as the ground state within the triplet manifold.
The stability analysis may show ou, whether you did converged the lowest triplet state, or not.
Best wishes!
Thank you both Dr Sergei Malykhin and Dr Marcin Andrzejak.
May i ask a clarification question: Lets say, I try to optimized the triplet excited state, using Unrestricted KS approach (say UB3LYP, spinmultiplicity = 3). Normally, i check stability after it convert with keyword "stable". The result always is stable.
So, what if, the result is unstable. What i need to do next, if im looking for optimized triplet state.
Thank you.
This may be difficult in cases, in which the lowest triplet state is not represented to a good approximation by a single configuration (single Slater determinant). In such a case, TDDFT may give different results than the UB3LYP with set orbital occupation.
In that case, I'd suggest the LR-CC2 method, which is relatively cheap (scales with the N^5 with the number of orbitals) and if only the GROUND state is singly-configurational, usually gives very good excitation energies and good geometries.
Good Luck
Marcin
Thank you, Dr Marcin. I hope it wont happen to my compounds. So far, the stability checks all report stable. If it happens, i will lock back to your suggestion and do more reading regarding that issue.
Thank you!
-Mer-
Actually, stability check is just CIS procedure for the HF reference or TDDFT (RPA) for the KS wavefunction. The instability appears when some eigenvalue of the CIS(RPA) matrix is lower than eigenvalue of the reference state. Assuming the reference as zero, negative eigenvalue indicates instability. Think about these eigenvalues as squares of the vibrational frequencies and you will find pretty good analogy with geometry optimization check: to be sure that geometry is minimum you should not have imaginary frequencies. Of course, the hessian matrix calculation should be done in the same level of theory as geometry optimization. The same is true for wavefunction stability check. Therefore, at your level of theory this particular triplet is lowest only if its pass stability check.
Since stability check is actually cumbersome procedure, you may be interested in method of finding true ground state from the beginning. To achieve that, your initial guess should be BAD, that mean guess=core or something. The best option is completely randomized wavefunction, to be sure that initial guess has nonzero overlap with true ground state. Good guesses are good only if they overlap with true ground state, but you cannot be sure in advance that Gaussian offer you that kind of initial guess. By default, Gaussian optimized for speed of the SCF procedure, that means initial guess generated requires only 10-20 steps to converge. Guess=mix makes guess worse, but allows one to converge into broken symmetry biradical solution. On the other side, the bad guess results in bad SCF convergence.
Happily, there is solution. Instead of the ordinary DIIS (commutator-based DIIS) convergence accelerator, which suffers from the bad guesses, but converge fast, there is EDIIS (energy-based DIIS) which has guaranteed convergence, but slow. Since Gaussian 09 EDIIS+CDIIS combination is used. You may tune this combination from speed(default) to guaranteed ground state convergence. In the difficult cases I prefer the following combination: Guess=Core or Guess=mix together with iop(5/22=6032) scf=(MaxCycles=500). This turns on EDIIS from the beginning and switches to CDIIS only if commutator is pretty small (10**-6) to be sure that we achieve ground state.
i hope this information will be helpful.
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