LDA and GGA Exchange Functionals

Containing no artificial terms added only to satisfy specific fundamental conditions or physical properties. Improvements by superficial operations narrow the versatility and applicability of functionals by contrast. 

Taking into account physical corrections with no additional operation. If functionals lack the versatility to take into account all physical corrections, like those given in Chap. 6 without modifying parameters, they would fade out in a short time. 

In this chapter, exchange-correlation functionals are classified by then-formulations, and the features and problems of these functionals are considered on the basis of the above criteria. In particular, the numbers of semiempirical parameters are mentioned. Since an enormous number of exchange-correlation functionals have been developed thus far, it is difficult to introduce all of them encyclopaedically. I therefore focus on the major functionals, which have taken into account the physical corrections given in Chap. 6 and are implemented in the predominantly used quantum chemistry calculation programs, e.g., Gaussian09 and GAMESS (current 2014). 

GGA exchange functionals traditionally have a general form using a dimensionless coefficient which is defined by 

This Kc is usually expressed with the dimensionless parameter Xa, 

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