Convergence Questions

• General Issues
• Geometry Optimization Issues
• Special Issues with Transition State Searches
• Wave-function (SCF) Convergence Issues
• Converging the CPHF in frequency/IR calculation (the "iterz" error)
• Concluding Remarks
• Some Common Questions
  1. I ran a geometry optimization followed by a frequency calculation and it showed a negative eigenvalue. Doesn't this mean I've found a transition state and not a minima?
  2. A geometry optimization ran out of cycles, how do I restart it?
  3. What are the specifics of the CONVERGE keyword?
  4. I got a 'CnV slipped through' error message. What should I do?
• Keyword List

General Issues

• The geometry is poor,
• The charge is wrong,
• The multiplicity is wrong.
• Symmetry is causing a problem.

• Geometry
  Examine the molecule carefully. Try the same calculation at a simpler theory level or with a smaller basis set. If the lower theories work, they are likely good starting points for advanced theories. (For quantum chemical calculations, theoretical approaches are listed in order of increasing complexity: Semi-Empirical < Hartree-Fock < Density Functional < Configuration Interaction and Moller Plesset < Wave Function Based Correlated).
  
  Examine the molecule's current geometry carefully; do the bond distances and angles seem correct? (Or nearly correct?) Molecular Mechanics can sometimes produce strange results when metals are involved. Semi-Empirical is fast and often very good, but it also may also suffer from poor approximations, and may not be good enough for your molecule.
  
  Another common problem is that the current geometry may have a symmetry that is not a reasonable energy minima in the theory you are attempting to use. Turning "Symmetry" off is sometimes appropriate; this can be done by using the IGNORESYMMETRY keyword. Sometimes it is also necessary to physically break symmetry by slightly changing bond distances or angles. (Watch the symmetry label in the bottom right of the screen to determine if your changes are large enough.)
  
  
• Charge
  Make sure to count electrons and look for radicals in your molecule. The charge and number of unpaired electrons specified in the Calculation Dialog must be consistent with the molecule.
  
• Unpaired Electrons
  Are there unpaired electrons? If so, you may want to choose an unrestricted calculation by typing either SCF=UNRESTRICTED or SCF=RESTRICTED keyword in the options field in the Calculations dialog.
  If your system includes a metal atom, ask yourself if the metal is in a high or low spin state. Hemoglobin complexing with Carbon-dioxide and molecular Oxygen are common examples where spin states need to be accounted for. Make sure the multiplicity is consistent with the state you desire. In questionable configurations one may need to try differing number of unpaired electrons to see which one has the lowest calculated energy. (i.e. 0,2,4... or 1,3,5... etc. depending on whether there is an even or odd total number of electrons.)
  
  
• Symmetry
  The use of symmetry can dramatically speed up calculations on small symmetric molecules. However attempting to use symmetry can sometimes cause difficulty in convergence. Use the IGNORESYMMETRY keyword to disable the use of symmetry. As mentioned in the geometry section, it is sometimes useful to physically break symmetry.

Geometry Optimization Issues

• Re-examine the geometry.
  If the starting geometry is poor, some new chemistry might be occurring that you do not anticipate. For example, if a hydrogen is too close to a nitrogen, a bond may form (that you don't want) Recall that the bonds drawn on the screen mean absolutely nothing to the quantum calculations.
  
  At times the job may be converging normally, just slowly, and one only needs to resubmit a job that has 'run out of cycles'. But before you resubmit, examine the current conformation of the molecule. Jobs that run out of cycles do so because atoms have moved a lot during the geometry optimization. Chances are that some chemistry is occurring (a bond forming or breaking) that you may not desire.. This could be due to poor initial geometry (see above) or a poor initial Hessian (discussed below). Adding the GEOMETRYCYCLES=xxx or OPTCYCLE=xxx (where xxx is some large number) keyword should keep the job from terminating early.
  
  It is also possible that the algorithm is seeking the minima (or transition state) at a higher level of precision than you need. You can change the precision criteria by using the GRADIENTTOLERANCE=x or DISTANCETOLERANCE=x. (TOLG=x or TOLD=x are shorter versions of these keywords.)
  
  
• Check the Hessian
  The most common problem with geometry optimizations is that the default Hessian is poor. Usually a molecular mechanics Hessian saves many geometry optimization steps for standard systems, and semi-empirical Hessians are good for transition searches. (These are the defaults). But these defaults can sometimes be poor approximations for molecules outside their range of parameterization.
  
  You can choose a conservative Hessian with the HESS=UNIT keyword. While this will typically avoid bad modes in the Hessian, it does slow the optimization procedures.
  
  The best Hessian is one generated at the same theory level as the one you are attempting use for optimization. Often this is too expensive (from a time perspective) to calculate, but if you are having trouble you may want to generate this high quality Hessian. This can be accomplished by doing an energy calculation with the IR button checked. (This will generate a Hessian.) When this completes you can resubmit the job as a geometry optimization (or transition state optimization).
  
  
• Start simple
  It is always good advice to start by using a lower theory level. In general we suggest using the Minimizer (the Minimize button in the Spartan interface uses molecular mechanics to reduce strain energy and 'clean up' molecules that have been constructed by hand), and then (perhaps) doing a quick geometry optimization at a simple level of theory such as semi-empirical or Hartree-Fock with a small basis (3-21G*). There are, however, instances when this might not be a good idea; for example, one should NOT typically use the Minimizer before submitting a Transition State Geometry optimization. There are also cases where a lower level theory level may simply produce poor results on your type of molecule. After some hands-on experience you will know better than anyone else what works for your favorite class of molecules.
  
  Another approach is useful when building large molecules:
  1. Start with a small core of your molecule and optimize it at the theory you desire.
  2. Then add some atoms to the core, (perhaps minimizing the new atoms with molecular mechanics, while 'freezing' the original core)
  3. Optionally, you may want to freeze the core atoms and minimize the new atoms at a lower theory level. You can use molecular mechanics in the Spartan interface (the Minimize button), or any other theory from the Calculations dialog. (Make sure to select the "Frozen Atoms" box next to the words "Subject To:" in the calculations dialog.)
  4. Then submit the entire molecule for a final geometry optimization. Make sure to deselect "frozen atoms" in the calculations dialog.
  You can repeat this procedure until the full molecule is complete. The above approach is often useful when searching for transition states.
  
  
• A word about coordinates
  While the simplest coordinate system for geometry optimization is Cartesian, Spartan will commonly use an internal coordinate system (sometimes referred to as "redundant internal coordinates" [RIC] or "delocalized internal coordinates"). This takes into account the standard bonding of tetrahedral sp3 and planar-like sp2 systems. This also speeds up geometry optimizations by more than a factor of 2 for typical organic systems. There are cases where the internal coordinate system can cause a problem, particularly when the geometry changes significantly during the optimization or in some high-coordination systems. In these cases you may want to turn the default behavior off by using the NOGEOMSYMMETRY keyword (entered into the Options line of the Calculations dialog).
  
  
• The molecule doesn't have the exact symmetry I want.
  It can be difficult int Spartan to maintain the exact symmetry. Often there is not much you can do but the FORCESYMMETRY keyword will try harder to maintain symmetry. It is also required to start from "nearly exact" symmetry in order to maintain symmetry. The best way to do this is by minimizing in the builder by clicking the minimize button. If this method does not produce the right starting symmetry (shown in the lower right of the Spartan window) running higher end theories will likely never find an exact symmetry.

  Spartan symmetry algorithms require very high precision to determine symmetry (more than 1 part per million). If the molecule "looks" symmetric but Spartan doesn't report that it is the symmetry you wanted, it is probably close enough for all practical purposes (i.e. energy/frequencies etc.) but just not to the very high tolerances required by Spartan to report. No harm is done by being slightly numerically off in the geometry.

  It is worth mentioning that it is likely that even given a starting geometry that is perfectly symmetric the calculation can lose the symmetry. While this can happen because the symmetric position is in fact meta-stable, it can also happen because the math (and mathmatical approximations used in Spartan) will lose symmetry. For example in DFT the the numerical grids used to calculate forces may not have the same symmetry as the global molecule. There are other similar approximations in calculating the math that can lead to small errors in the forces that may eventually lead to the geometry leaving the precise symmetry required by our symmetry detecting logic.

  Warning on symmetry use: Because (many) symmetry operators are numerically approximate, when a certain operation (say rotation) is right on border of being satisfied, some parts of the code might think there is symmetry while another part might think there is no symmetry. When this happens disasterous things can happen. Usually (but not always) this has obvious affects such as forces becoming unreasonable. So care needs to be taken when forcing symmetry.

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.

• Likely the first keyword to try is the CONVERGE keyword. This changes a number of internal flags which often leads to better SCF stability, at the cost of slower performance. For more information see below for more specifics.
• If it looks like the system is converging, just slowly, you may simply need to be patient and let the optimization continue on its own. Use the SCFCYCLE=xxx to increase the number of SCF cycles to try before the program gives up.
• If the SCF looks like it has stopped converging, but the "Error" is not decreasing, you may need to change the tolerance. Setting SCFTOLERANCE=HIGH or SCFTOLERANCE=VERYHIGH increases internal accuracy. While this may make the calculation more internally consistent (thus improving convergence), it will demand lower error (thus demanding more cycles). Conversely SCFTOLERANCE=LOW will decrease the tolerances, usually speeding up the calculation at the cost of a significant reduction in precision. This is not advised for geometry optimizations.
• If you can live with a less accurate result, you can allow the convergence algorithm to stop earlier by using the previously mentioned SCFTOLERANCE keyword with a tolerance level. For example, using SCFTOLERANCE=6 keyword (default value is 7). Note the format of SCFTOLERANCE is flexible; "0.000001", "1.0e-6", and "6" all mean the same thing. If you increase SCFTOLERANCE above 7, you should also increase THRESH=x to a value that is at least 2x greater than the new SCFTOLERANCE.
• For difficult cases, it is sometimes helpful to combine the SCFTOLERANCE=LOW with the CONVERGE keyword. This will increase the precision of the integrals, while at the same time requiring lower convergence. As mentioned above this is not advised for geometry optimizations, and if used should only be done for the first few geometry cycles.
• It is possible that the initial wave function is bad. You can change the initial guess with the GUESS=CORE keyword. If you have an open shell system you may need to add the MIX keyword to construct a better guess. For some systems with metals the default guess is already a core guess. In this case you may achieve better results with the GUESS=SAD keyword. (SAD stands for "superposition of atomic densities", a quick method for generating an initial wave function.)
• Sometimes molecules with diffuse basis sets can cause unique problems. This can be attributed to "nearly linearly dependent" basis functions. Spartan automatically checks for linear dependence in the basis set, and will project out near-degeneracies, if they exist. This will result in there being slightly fewer molecular orbitals than there are basis functions. This is done by considering the eigenvalues of the overlap matrix. Very small eigenvalues are an indication that the basis set is close to being linearly dependent. The size at which the eigenvalues are considered to be too small is governed by the option keyword BASIS_LIN_DEP_THRESH. By default this is set to 5, corresponding to a threshold of 10^-5. This has been found to give reliable results, however, if you have a poorly behaved SCF, and you suspect there maybe linear dependence in your basis set, the threshold should be increased.
• As a last resort, you may need to adjust the details of the algorithm itself. This is an 'art form', with no hard and fast rules (at least not yet discovered. When they are discovered we will put them into the code explicitly so that the next generation of users will not have to deal with this level of detail.).
  
  Some relevant keywords are:
  • DIIS=SCF_ALGORITHM or DIIS=DIIS_GDM
  • DIIS=x where x is the dimension of the DIIS space. or NODIIS to turn the standard algorithm off.
  • If you are using Semi-Empirical methods (such as PM3 or PM6) some useful keywords are:
    
    • USEPSEUDO, NOPSEUDO to turn on and off a fast diagonalization method.
    • DAMP=x and NODAMP to turn damping on and off. (x is a number between 0.0 and 1.0.)
  • For HF and DFT methods:
    
    • VARTHRESH=4 ignore fewer integrals. Default is 3.
    • SCF_ALGORITHM=x where x can be one of DIIS, DM, DIIS_DM, GDM, DIIS_GDM or ROOTHAAN
  • DFT only keywords are:
    
    • BIGGRID or VERYBIGRID to choose a more accurate (and slower) electron density grid.
      
    • It should be noted that due to the numerical nature of the DFT calculation the numerical results are often not as stable as HF calculations. You may have to live with smaller tolerances in both the SCF calculation and in geometry optimizations (specifically in the uncertainty of the forces/gradients).
• During optimization runs it is sometimes common to have problems with SCF convergence on the first step, after which falling back to the default convergence parameters is acceptable. In this case in may be handy to use the GUESS= keyword. For example
  GUESS=B3LYP,6-31G*,DIIS~GDM,SCFCYCLES~900,SCFTOLERANCE~LOW
  In this example the comma-separated keywords as passed only to the "guess" step of the calculation. The SCF convergence algorithm falls back to the default values during the optimization steps.

Concluding Remarks

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:

   • The frequency calculation and the geometry minimization must be at the same theory level, and with the same basis set.
   • You are *almost* at the minima but the gradient is not sufficiently small.
     In this case the lowest eigenvalues are not that meaningful. If you suspect this is the case, you should be able to double check this by resubmitting the molecule with another geometry optimization and with the gradient tolerance increased a bit. As you are starting this new optimization with a very high quality Hessian you will likely fine tune the minimization in just a few optimization cycles. The energy and the maximum gradient should decrease and the final frequency calculation will show no negative eigenvalues, indicating us that you are indeed at a minima.
   • For some reason the Minimizer found a transition state.
     Many times this is due to a symmetry issue. It may also be that your starting configuration was very close to a transition state, and the minimizer found that transition state (with a zero gradient/force) rather than the minima you were looking for. If this is the case you should physically modify the geometry a bit and submit the job again.
   • A less common explanation might be that the Hessian is not very accurate. In this case you might see a few very small frequencies that (numerically) are very close to zero. This can be the case for very large molecules, and most often occurs with DFT methods due to the inherent numerical approximations used in DFT as well as the numerical electronic grid used.
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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.

   • For Semi-Empirical jobs, the CONVERGE keyword is equivalent to DAMP=0.75, DIIS=7, and NOPSEUDO.
   • For all other quantum mechanics jobs, it is equivalent to VARTHRESH=0, THRESH=0 SMALL_PROD_XCMAT=10 and MAXSCF=15.
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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

Keywords mentioned