# Custom-defined functionals in Gaussian 09

As stated before 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 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. 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).