Gaussian - Using Hybrid Functionals

In summary, B3LYP is a hybrid functional that uses a combination of HF and DFT methods for calculations. The proportions of each method can be adjusted, but this should not be done without a specific purpose or goal in mind. To modify the proportion of HF used in B3LYP, one would need to alter the route section, specifically the terms represented by P1 and P2. This can be a complex process and it is important to have a good understanding of the mathematics behind it.
  • #1
mycotheology
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0
I read that B3LYP is a hybrid functional which uses some HF method and some DFT method for its calculations. According to this page:
my professor told me that you can set the proportions of each method that the B3LYP uses yourself, so for example you can make it so it uses 70% HF and 30% DFT or 20% HF and 80% DFT etc. I'm trying to figure out how to do that. More specifically, I want to alter the proportion of the HF and slater functionals that B3LYP uses. According to this page: www.gaussian.com/g_tech/g_ur/k_dft.htm
the route section for the B3LYP method is as follows:
#P BLYP IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)
I'm confused about what these 3 terms represent. If I wanted to increase the amount of HF that B3LYP uses, what would I change in that route section? In the Gaussian manual, they say that Gaussian can use any model of the form:
P2EXHF + P1(P4EXSlater + P3ΔExnon-local) + P6EClocal + P5ΔECnon-local
heres a screenshot of this section of the manual:
63e39557295d4a626a4da1104b2dd2a8.png

Anyone know how I can alter the amount of HF used by B3LYP by altering that route section?
 
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  • #2
The first thing to do is to stop thinking about hybrid functionals in terms of B3LYP. B3LYP is nothing more than an instance of a hybrid functional with the amount of exact exchange and other DFT parameters chosen to best fit experimental data. If you change those values at all, you're no longer talking about B3LYP, you're talking about mixing in Becke's exchange with Lee-Yang-Parr correlation to create your very own "mycotheology" functional.

The second thing to do is to ask why you're doing this and what you expect to get out of it. It's not as if there is any "right" amount of exact exchange to use in DFT to get the "best" functional for every case. If there were, it would have been found long ago. You can either fit your coefficients to experimental data like Becke, Lee, Yang and Parr or you can choose the amount based on purely physical grounds as in the case of the PBE0 functional (20% exact exchange and 80% PBE exchange to match perturbation theory arguments), but just playing around with it isn't going to do much but give confusing results. If you're trying to find the amount of exact exchange that best fits known data to then explore an unknown system with the best possible functional optimized for that type of system, then that's great. But just changing it to change it is a waste of time.

Third, what's the deal with your prof again? What's the goal of your study project and why isn't he/she answering these question for his/her student?
 
  • #3
Another brilliant explanation, thanks! Well what I'm doing is trying to find a functional model that can accurately model dinuclear copper complexes. According to my professor, the Cu-Cu bond throws Gaussian way off due to its particular Coulombic interactions. He tried a few different methods and he says Hartree-Fok causes the Cu-Cu bond to expand, while the slater exchange functional causes it to contract. He assigned me this project (the task of coming up with a hybrid functional that accurately models this type of molecule) because he knows I can program and thus, write a program to automatically generate input files and find the best output file etc.

The particular class of compounds he's researching are big and I'd need a supercomputer to run optimisations on it so I need to find experimental data for a simple Cu-Cu compound and run calculations on that instead. The programming part I have covered, I just need to know what I'm doing with these hybrid functionals. I'm guessing from what he told me that I need to test different ratios of HF and slater exchange. He suggested I modify the B3LYP method to do this but I don't know what part of this route section:
IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)
I need to modify. I know that the first term sets P1 to 1.0 and P2 to 0.5 but I don't know what P1 and P2 represent. Maths isn't a strong point of mine. From this equation:
P2EXHF + P1(P4EXSlater + P3ΔExnon-local) + P6EClocal + P5ΔECnon-local
it appears that P2 is the amount of HF used. The part in brackets has me baffled though, what is P1?
 
  • #4
mycotheology said:
Another brilliant explanation, thanks! Well what I'm doing is trying to find a functional model that can accurately model dinuclear copper complexes. According to my professor, the Cu-Cu bond throws Gaussian way off due to its particular Coulombic interactions. He tried a few different methods and he says Hartree-Fok causes the Cu-Cu bond to expand, while the slater exchange functional causes it to contract. He assigned me this project (the task of coming up with a hybrid functional that accurately models this type of molecule) because he knows I can program and thus, write a program to automatically generate input files and find the best output file etc.

The particular class of compounds he's researching are big and I'd need a supercomputer to run optimisations on it so I need to find experimental data for a simple Cu-Cu compound and run calculations on that instead. The programming part I have covered, I just need to know what I'm doing with these hybrid functionals. I'm guessing from what he told me that I need to test different ratios of HF and slater exchange. He suggested I modify the B3LYP method to do this but I don't know what part of this route section:
IOp(3/76=1000002000) IOp(3/77=0720008000) IOp(3/78=0810010000)
I need to modify. I know that the first term sets P1 to 1.0 and P2 to 0.5 but I don't know what P1 and P2 represent. Maths isn't a strong point of mine. From this equation:
P2EXHF + P1(P4EXSlater + P3ΔExnon-local) + P6EClocal + P5ΔECnon-local
it appears that P2 is the amount of HF used. The part in brackets has me baffled though, what is P1?

The wiki page has a good explanation of what goes into b3lyp and what they mean:
http://en.wikipedia.org/wiki/Hybrid_functional#B3LYP
Otherwise if you want a better source, try, say:
Citation: J. Chem. Phys. 117, 1441 (2002);

Still, I don't see why you're messing with b3lyp. It's parametrized for organic systems, not transition metals. It has been shown that exact exchange helps for those types of systems, but not the way B3LYP does it (it's the LYP part, not the Becke88 part). The following papers by Buhl et al. are exactly on point for this:
J. Chem. Theory Comput. 2006, 2, 1282-1290
J. Chem. Theory Comput. 2007, 3, 2234-2242
J. Chem. Theory Comput. 2008, 4, 1449–1459
As you'll see, exact exchange is much better than not, but B3LYP is nowhere near the best for these systems.

Finally, transition metal systems are tricky. Finding the right functional basically comes down to getting the right proportions of cancellation of errors to give an accurate picture of the systems. Often times this leads to better performance than "higher level" methods like MP2 or multi-reference, but it often depends on the property you're interested in. I'd highly recommend you check out this paper before going too far:
J. Chem. Phys., Vol. 112, No. 2, 8 January 2000
It might save you some time.
 

FAQ: Gaussian - Using Hybrid Functionals

1. What is a Gaussian hybrid functional?

A Gaussian hybrid functional is a computational method used in quantum chemistry that combines the accuracy of density functional theory (DFT) with the efficiency of molecular orbital theory (MO). It is based on the Gaussian distribution and uses a combination of both DFT and MO methods to calculate electronic structures and properties of molecules.

2. How does a Gaussian hybrid functional work?

Gaussian hybrid functionals work by combining the DFT energy functional with a fraction of the Hartree-Fock exchange energy. This allows for a more accurate description of electronic correlation and improves the accuracy of results compared to traditional DFT methods.

3. What are the advantages of using a Gaussian hybrid functional?

The main advantage of using a Gaussian hybrid functional is its ability to accurately predict electronic structures and properties of molecules. It also allows for the inclusion of dispersion forces, which are often important in weakly interacting systems. Additionally, Gaussian hybrid functionals are computationally efficient compared to other high-level quantum chemistry methods.

4. What are some common Gaussian hybrid functionals?

Some common Gaussian hybrid functionals include B3LYP, PBE0, and M06. These functionals differ in the way they combine DFT and Hartree-Fock methods, as well as the percentage of exchange energy used in the calculation. Each functional may be better suited for certain types of molecules or properties.

5. How do I choose the right Gaussian hybrid functional for my research?

The choice of Gaussian hybrid functional will depend on the specific properties or molecules being studied. It is important to consider the strengths and limitations of each functional, as well as any previous studies that have used similar functionals for similar systems. It is also recommended to compare results from different functionals to ensure accuracy and reliability of the final results.

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