Density-functional theory systematic improvement

There is no systematic way in which the exchange correlation functional Vxc[F] can be systematically improved in standard HF-LCAO theory, we can improve on the model by increasing the accuracy of the basis set, doing configuration interaction or MPn calculations. What we have to do in density functional theory is to start from a model for which there is an exact solution, and this model is the uniform electron gas. Parr and Yang (1989) write... 

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. 

One of the drawbacks with density functional theory is that there is as yet no systematic way in which to improve a particular method, in a fashion similar to, e.g., MBPT or Cl expansions used in HF-theory. By necessity, the application of DFT based methods has to be pragmatic, and each functional form must be assessed on its own merits and improved models suggested. At present, a large body of literature is becoming available on the performance of the abovementioned correction schemes, that will form the basis for improved versions, entirely new functionals, or new combined schemes along the lines suggested through the B3 hybrid functional. 

During the last 10-20 years, a large number of efficient theoretical methods for the calculation of linear and nonlinear optical properties have been developed— this development includes semi-empirical, highly correlated ab initio, and density functional theory methods. Many of these approaches will be reviewed in later chapters of this book, and applications will be given that illustrate the merits and limitations of theoretical studies of linear and nonlinear optical processes. It will become clear that theoretical studies today can provide valuable information in Are search for materials with specific nonlinear optical properties. First, there is the possibility to screen classes of materials based on cost and time effective calculations rather then labor intensive synthesis and characterization work. Second, there is Are possibility to obtain a microscopic understanding for the performance of the material—one can investigate the role of individual transition channels, dipole moments, etc., and perform systematic model Improvements by inclusion of the environment, relativistic effects, etc. 

Perturbation and coupled cluster theories (e.g., MP2 or CCSD) provide correlation corrections. Density functional theory (DPT) appears to offer the best of all worlds, correlation-quality results at single-determinant prices. However, there is always a limit somewhere. The choice today seems to be between correlated methods with large basis sets, such as CCSDT, which systematically approach the "correct" answer at appreciable cost, and DFT, with its relatively economical efficiency, but which cannot be systematically improved (5). 

---