Custom-defined functionals in Gaussian 09

As [stated before](https://chemistry.stackexchange.com/questions/39411/definition-of-the-b3lyp-functional-in-common-qc-programs) I want to try out custom-defined functionals. Besides the question about B3LYP itself, there is another related question.


Short excerpt:



> 
> $$\text{XC-Functional}=a E\_x^\text{local}+(1-a)E\_x^\text{HF}+b E\_x^\text{non-local}+c E\_c^\text{non-local}+(1-c) E\_c^\text{local}$$
> 
> 
> The Gaussian documentation for DFT inputs specifies how one could change the amounts of each "sub-functional" by using the IOp-Statements through:
> 
> 
> IOp(3/76=mmmmmnnnnn) IOp(3/77=mmmmmnnnnn) IOp(3/78=mmmmmnnnnn)
> 
> 
> Where `mmmmm` and `nnnnn` will get divided by 10000 and `3/76`=$P\_1P\_2$, `3/77`=$P\_3P\_4$ and `3/88`=$P\_5P\_6$. Those $P\_{1,..,6}$ values are part of the following equation, which is a modified version of the equation above.
> 
> 
> $$\text{XC-Functional}=P\_2 E\_X^\text{HF} + P\_1 \left(P\_4 E\_X^\text{Slater} + P\_3\Delta E\_x^\text{non-local}\right) + P\_6 E\_C^\text{local} + P\_5 \Delta E\_C^\text{non-local}$$
> 
> 
> 


Now [Gaussian's description site about DFT](http://gaussian.com/g_tech/g_ur/k_dft.htm) tells that one simply has to choose one exchange and one correlation functional, i.e. B and LYP. But then B would be used for $E\_x^\text{non-local}$ and LYP probably for $E\_c^\text{non-local}$.


Does that mean, that the $E\_c^\text{local}$-part


* cannot be defined,
* is always the VWN functional as in B3LYP, or
* is also the chosen correlation functional?




Take a look at the [IOp manual](http://www.gaussian.com/g_tech/g_iops/iops2.pdf). Under IOp(3/74),



> 
> **IOp(3/74)** Type of exchange and correlation potentials.
> 
> 
> * **-5** Becke3 using VWN/LYP for correlation.
> * **02** Lee-Yang-Parr correlation.
> * **05** VWN 80 (LSD) correlation.
> * **200** Hartree-Fock-Slater exchange (Alpha = 2/3).
> * **400** Becke 1988 exchange.
> 
> 
> So 100 is Hartree-Fock, 200 is Hartree-Fock-Slater, 205 is Local Spin Density, and 402 is BLYP.
> 
> 
> 


They're unclear about it, but this means you can take the "sum" of a 1- or 2-digit number (which specifies the correlation) and a 3- or 4-digit number (which specifies the exchange) to build an exchange-correlation functional. So, `IOp(3/74=-5) == IOp(3/74=402)`, and an identical way to define B3LYP is


`IOp(3/74=402) IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)`



> 
> Does that mean, that the $E\_{c}^{\text{local}}$-part
> 
> 
> * cannot be defined,
> * is always the VWN functional as in B3LYP, or
> * is also the chosen correlation functional?
> 
> 
> 


Looking at the available correlation functionals (incomplete, these are the lowest few),


* **01** VWN5
* **02** LYP
* **03** P81 (PL in keyword list)
* **04** P81 + P86
* **05** VWN3
* **06** VWN3 + P86
* **07** OS1
* **08** PW91
* **09** PBE
* **10** VSXC
* **11** Bc96
* **18** VWN5 + P86
* **19** LYP + VWN5 for scaling


your choices for *local* correlation functionals are rather limited. Either you choose a correlation functional that's purely local (VWN3, VWN5, or P81), or a non-local/gradient-corrected functional which in Gaussian all seem to have the local component as part of their definition (as in LYP), or they're forcibly combined (as in P86).


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