Convergence criterion

A typical test for convergence is Ak°H TOL where TOL is a user-specified tolerance. This test is suitable only when the unknown parameters are of the same order of magnitude. A more general convergence criterion is 

Determine p using the bisection rule and obtain k(j l,=k,J)+ pAk0 0 

Continue until the maximum number of iterations is reached or convergence 

Compute statistical properties of parameter estimates (see Chapter 11). 

In summary, at each iteration of the estimation method we compute the model output, y(x kw), and the sensitivity coefficients, G for each data point i=l.N which are used to set up matrix A and vector b. Subsequent solution of the linear equation yields Akf f 1 and hence k j+l) is obtained. 

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The AFC method does not have the same demanding convergence criteria as the FLAPW method but yields physically equivalent results [69]. 

Calculations using the semiempirical PM3 method with standard convergence criteria of 0.0003 aii on the maximum component of the gradient vector and either an energy change from the previous cycle of < 10 hartree or a maximum predicted displacement for the next step of < 0.0003 au. 

The next step will dciermin e optim i/ation convergence. If the criteria are satisfied, HyperCh em will stop at this point, having found theposition ofihc transition state. If convergence criteria are n ot... 

In setting up an optimization calculation, you can use two convergence criteria the root-mean-square gradient and the number of optimization cycles. 

Concerning the VDW parameters, the ability to directly apply previously optimized values makes convergence criteria unnecessary. If VDW parameter optimization is performed based on pure solvent or crystal simulations, then the heats of vaporization or sublimation should be within 2% of experimental values, and the calculated molecular or unit cell volumes should be also. If rare gas-model compound data are used, the references cited above should be referred to for a discussion of the convergence criteria. 

An optimization is complete when it has converged essentially, when the forces are zero, the next step is very small, below some preset value defined by the algorithm, and some other conditions are met. These are the convergence criteria used by Gaussian ... 

The predicted energy change is displayed, but it is not one of the convergence criteria. 

III (this option says to use full convergence criteria throughout the SCF computation,... 

We will also use the results of the frequency job in the IRC calculation we ll do next. This job will enable us to verify that this transition structure connects the two minima that we think it does, and we use the keyword IRC to request it. By default, the calculation takes 6 steps in each direction, where each step corresponds to a g. jinetry optimization. However, the calculation will stop searching in a given direction once its convergence criteria are met, and an IRC calculation does not necessarily step all the way down to the minimum. 

We specified tight SCF convergence criteria for all jobs (SCF=Tight). Here are the results of our calculations, as well as the computed and observed energy differences ... 

If the ecjuations have the proper characteristics, the iterative process will eventually converge. Commonly used convergence criteria are of two types ... 

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