Density-functional theory systematic error

Some density functional theory methods occasionally yield frequencies with a bit of erratic behavior, but with a smaller deviation from the experimental results than semiempirical methods give. Overall systematic error with the better DFT functionals is less than with HF. 

Vibrational Spectra Many of the papers quoted below deal with the determination of vibrational spectra. The method of choice is B3-LYP density functional theory. In most cases, MP2 vibrational spectra are less accurate. In order to allow for a comparison between computed frequencies within the harmonic approximation and anharmonic experimental fundamentals, calculated frequencies should be scaled by an empirical factor. This procedure accounts for systematic errors and improves the results considerably. The easiest procedure is to scale all frequencies by the same factor, e.g., 0.963 for B3-LYP/6-31G computed frequencies [95JPC3093]. A more sophisticated but still pragmatic approach is the SQM method [83JA7073], in which the underlying force constants (in internal coordinates) are scaled by different scaling factors. 

From a more quantitative point of view, it is more difficult to achieve accurate computations for DPEs than for PAs of neutral substrates, because molecular anions are involved in the former case. However, when using second-order perturbation theory (MP2), a coupled-cluster theory (CCSD(T)) or a density functional theory (DFT/B3LYP), in conjunction with a moderate atomic basis set including a set of diffuse and polarization functions, such as the 6-3114—FG(d,p) or cc-aug-pVDZ sets, the resulting DPE errors appear to be fairly systematic. To some extent, the accuracy rests on a partial but uniform cancellation of errors between the acid and its conjugate base. Therefore, use of appropriate linear regressions between experimental and calculated values allows the DPEs for new members of the series to be evaluated within the chemical accuracy of 4=0.1 eV or 4=10 kJmoD. ... 

The aim of the practical assignments for Quantenchemie is to enable the students to perform their own ab initio quantum chemical studies using off the shelf application software packages. There is also the goal to prepare the students to critically read the scientific literature in this area of research. Under this mission, we designed a set of problems which illustrates the capabilities of the different methods and the systematic errors involved (basis set truncation, electron correlation, thermal corrections, etc.) on a broad (but not systematic) range of chemical problems. Towards the end of the course only, the level of theory applied exceeds the levels of second order perturbation (MP2) or density functional theory. This also reflects the time limits imposed on the class (90 minutes per unit 7 units total no homework assignments). 

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