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A calculation aborts with the message: dependent basis. It means that for at least one k-point in the BZ the set of Bloch functions, constructed from the elementary basis functions (atom-centered and plane waves, if applicable) is so close to linear dependency that the numerical accuracy of results is in danger. To check this, the program computes, for each k-point separately, the overlap matrix of the Bloch basis (normalized functions) and diagonalizes it. If the smallest eigenvalue is zero, the basis is linearly dependent. (Negative values should not occur at all!). Given the limited precision of numerical integrals and other aspects in the calculation, you are bound for trouble already if the smallest eigenvalue is very small, even if not exactly zero. The program compares it against a criterion that can be set in input (key BASISDEPENDENCY).
If you encounter such an error abort, you are strongly advised not to adjust the criterion so as to pass the internal test - there were good reasons to implement the test and to set the default criterion at its current value. Rather, you should adjust your basis set. Generally speaking, you should remove one or more basis functions and maybe modify some of the (other) STO basis functions. The program prints information that helps you determine which basis functions should be modified/removed.
In the standard output file, after the error message, you will find a list of eigenvalues of the overlap matrix. If only the first is smaller than the threshold, you should remove one basis function. If more eigenvalues are very small, it is likely that you have to remove more than one function, although you can of course try how far you can get by eliminating just one.
Next the program prints the so-called Dependency Coefficients: a list of numbers, one for each basis function. Those with a large value are the suspicious ones. If you find two coefficients that are significantly larger than the others, you should replace the two corresponding functions by one. Easiest is to remove one of them (take the one with the bigger coefficient). If one of them is a numerical orbital from Dirac and the other an STO, remove the STO. If both are STOs, remove one and replace the other by some kind of average (regarding the radial characteristic: exponential factor and power of radial coordinate).
To identify how the functions in your input correspond to the list the underlies the series of Dependency Coefficients, you have to set up the list of basis functions as follows:
- Consider an outer loop over all atom TYPES. These correspond, in order as well as in number, to the sequence of DIRAC keys in your input file.
- For each type, consider a loop over all atoms of that type, i.e. the atoms in the ATOM block corresponding to the DIRAC key at hand.
- For each atom, first write down all DIRAC basis functions, then all STOs. When writing down the functions, be aware that each entry in your input file specifies a function set, by the quantum number L and hence corresponds to 2L+1 actual basis functions.
- Regarding the DIRAC basis functions: they belong to the list of basis functions only if the key VALENCE occurs in the pertaining DIRAC input block. If not, no DIRAC functions of that type are included in the basis. IF the Dirac functions are included, you must omit the Core functions and include only the Valence functions from that DIRAC block. The first record in your DIRAC block with two numbers defines (by the first number) the total number of function sets in the DIRAC block (which you can verify by simple counting) and (by the second number) the number of Core function sets among them. The Core function sets, if any, are always the first so many in the list in the DIRAC block.
Since the program stops as soon as it encounters a dependency problem. This may happen for the first k-point. After you have adjusted the basis set following the above guidelines, you will have solved it. However, it may easily happen that the problem shows up again, but now for another (later) k-point, where other entries in the basis set may cause trouble. Do not think you have repaired the first problem incorrectly. Just repeat the procedure until you pass all k-points in the basis set construction without errors. Typically (as a last remark), although not necessarily, the first k-point may have a dependency problem from too many s-type functions, while other k-points may be more sensitive to the series of p-functions in your basis.