Convergence Questions

The algorithms in Spartan will typically perform well on most systems when solving quantum mechanical equations. However, there are times when one may see "convergence problems". What to do when this occurs? The following covers the typical areas to examine when a calculation has trouble converging.

The first question to ask is "Am I having problems converging the geometry, or the wave-function?" The answer to this question will lead to different sections of this FAQ below. The first section "General Issues" covers some topics which are relevant to both geometry and wave-function (SCF) convergence.

General Issues

Some common convergence issues: If you've made it this far, you have examined your molecule and believe everything is correct in the calculation setup. Now it's time to delve deeper into the calculation. The first thing to do is determine whether problems are related to the geometry optimization or the self-consistent field calculation (SCF) of the wave function. If you have one or more geometry cycles displayed in the output dialog, the problem is likely related to geometry optimization. (Of course, there may be exceptions, so examine the error message carefully.)

The following section includes several references to "keywords". Keywords are type-in options, to be entered in the "Options" field in Spartan's Calculation dialog. Keywords are NOT case sensitive. Multiple keywords are separated by spaces.

Geometry Optimization Issues

Special Issues with Transition State Searches

Spartan treats Transition State searches as a special case of geometry optimizations. Because of the flat nature of the potential energy surface and other unique characteristics of transition states, transition state geometry tasks can be more difficult to perform than the typical ground state geometry. The above discussion on geometry optimizations holds for transition state geometries. The strategy of starting small and working up to larger molecules and methods applies to transition state searching. However, for efficient transition state searches the importance of a good starting geometry and a good Hessian are especially critical.

A good starting geometry can be found using Spartan's transition state builder/searching feature. A number of examples of using this can be found in Chapter 11 of our Spartan Tutorial and User's Guide. (Also see the sections on Spartan Reaction Database and Transition States in Chapter 23 for additional information on these features.) Setting up an Energy Profile calculation is another way of getting a good starting point for transition state geometry tasks.

Once a good starting point is found a good Hessian is required. Often Spartan's default Hessian (a semi-empirical guess) is good enough. The best Hessian is obtained from an initial IR/frequency calculation. i.e. First do a single point energy calculation with the IR property checked. When this completes, examine the vibrations (Display Menu -> Spectra). Ideally there is one negative frequency (noted with an "i" in front of the frequency), and upon animating, this should look like motion along the reaction coordinate associated with the transition state. If the largest imaginary frequency is not what you expect, or if there are no imaginary frequencies, the starting geometry was not close enough to the transition state.

In very difficult cases I sometimes force a complete analytical/exact Hessian every few cycles. For example assuming the geometry is close to the actual transition state would:

  1. Do a single point energy with IR selected.
  2. Check to make sure there is only 1 negative eigenvalue, and that it looks right by animating it.
  3. Run a Transition State Geometry with the keyword OPTCYCLE=5 (or some small number). This job will (most likely) run out of optimization cycles.
  4. Go back to step 1 to get the real/exact hessian and repeat.

If at any point in step 2 you discover that there is no longer a good negative eigenvalue you need to adjust the geometry. One useful strategy is to do an Energy Profile calculation to find a rough TS. The SN2 Reaction of Bromide and Methyl Chloride tutorial and the Thermodynamic vs. Kinetic Control tutorial (from the Chemical Reactions  Activity provide good examples of this strategy.

Wave function (SCF) Convergence Issues

Gaining insight into SCF convergence issues is more difficult. The non-linear Schrödinger equation and the non-locality of electrons make it difficult to understand what is actually occurring. It is often useful to request progress data from the convergence process. This can be done by using the PRINTLEV=2 keyword, or examining the "Verbose Output". Examining this output can yield several clues, you should see both the energy and the "DIIS error" slowly decrease. We suggest you try some of the steps below and observe their results in the verbose output.

Converging the CPHF in frequency/IR calculation

Rarely, the calculation of the Hessian (frequency) will not converge and produces the "Out of Iterations- IterZ". This is usually due to precision problems so the CONVERGE keyword may help. If, after examining the verbose output, it seems reasonable that simply waiting longer will cause the job to converge, one can use the keyword SET_ITER=100 to let the algorithm continue 100 steps. (the default is 30.) One can also decrease the convergence criteria by using the SET_CONV=5 keyword. (The default is 6.)

Concluding Remarks

Computational Chemistry is a developing discipline. Quantum chemical calculation methods have matured to a level such that programs like Spartan can routinely provide results for molecular geometries, energies, and a host of calculated properties at a predictable and useful level of accuracy with very little user intervention. Chances are good that if you spend some time with the hints mentioned above, you will overcome any computational obstacles that your specific system presents. Since it is likely that you are focused on a finite class of molecules, when you uncover the approach that works on one system, it is likely that this will also work on similar molecules.

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Other Questions

  1. I ran a geometry optimization followed by a frequency calculation and it shows a negative eigenvalue. Doesn't that imply that I've found a transition state?

    Yes it does, If the gradient is zero. There are a few likely causes of this behavior:

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  2. A geometry optimization ran out of cycles. How do I restart?

    Simply resubmitting the job will continue the optimization. If you believe it will continue to take a lot of cycles, you can increase the maximum number of cycles with the GEOMETRYCYCLES= keyword. Running out of cycles usually implies that you had a bad starting guess, or that some unexpected chemistry is occurring (such as bond breaking). Review the Geometry optimization section for a more thorough discussion on what can go wrong and how to fix it.

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  3. What are the specifics of the CONVERGE keyword?

    The CONVERGE keyword behaves differently for different computational tasks.

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  4. I got a 'CnV slipped through' error message. What should I do?

    This error message implies that there is an approximate symmetry, but not exact enough. (Some internal round-off error in detecting symmetry has occurred.)

    Typically turning off symmetry with the IGNORESYMMETRY keyword will resolve the issue. Sometimes clicking the 'Minimize button' a few times will force the symmetry to be more exact and also solve the problem.

Useful keywords

Geometry Optimization Keywords
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Keywords mentioned

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Wavefunction Support
Author: Phil Klunzinger