When I was studying adiabatic methods (hybrids) the first to apply three parameters to correlation integral was Perdew, giving the B3PW91. Later, it was suggested to apply full correlation method (LYP) but the three parameters optimized was not change to fit to LYP and giving the B3LYP without new optimization.
Could be this change give extra errors in systems more complex than organic ones? This is the reason that B3PW91 give better results for metals than B3LYP?
Thank you very much.
Joaquim Maria Rius Bartra
4th Grade Chemistry.
Universitat Autònoma de Barcelona
Although this is not a real answer to your question, have a look at the attached link. However, they never give a reason as to why they did not optimise anything.
http://chemistry.stackexchange.com/q/27302/4945
It was optimized, but it takes time while researchers pick that up:
Global hybrids, which add a typically modest fraction of the exact exchange energy to a complement of semilocal exchange−correlation energy, are among the most widely used density functionals in chemistry and condensed matter physics. Here we briefly review the formal and practical advantages and disadvantages of global hybrids. We point out that empiricism seems unavoidable in the construction of global hybrids, as it is not for most other kinds of density functional. Then we use one to three parameters to hybridize many semilocal functionals (including recently developed nonempirical generalized gradient approximations or GGA’s and meta-GGA’s). We study the performance of these global hybrids for many properties of sp-bonded molecules composed from the lighter atoms of the periodic table: atomization energies, barrier heights, reaction energies, enthalpies of formation, total energies, ionization potentials, electron affinities, proton affinities, and equilibrium bond lengths. We find several new global hybrids that perform better in these tests than standard ones, and we correct some errors in literature assessments. We also discuss the representativity of small fitting sets and the adequacy of various Gaussian basis sets.
see details in:
http://pubs.acs.org/doi/abs/10.1021/ct100488v
Thank you very much. Your article is very clear and useful. Now I understand much better the difference. When I was studying this methods, the thing I don't understand is why the parameters are the same. I think that because after applying the Hellmann-Feynmann equation and solving the integral, if you use a different function for solving the correlation part, why the parameters that fits the function are the same than last one? The integral is no different with BLY than with PW91?
We show in a much earlier paper that practically the parameters are interdepenedent, so infinite number of linear combinations give practically the same result, and the key factor is the exchange mixing. The correlation mixing and gradient mixing can neutralize the effects of each other on the electron density:
http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1096-987X(199709)18:12%3C1534::AID-JCC10%3E3.0.CO;2-K/abstract;jsessionid=E7450CBDB8E7FA43000B20BC0FAB60DE.f02t01
B3LYP and B3PW91 are fundamentally different. PW91 is a gradient correction to the LSDA, so it is exact for homogenous electron gas (HEG). LYP is not. So the mixing formula is very different. Also the B3LYP uses the VWN3 (RPA) parametrization of the HEG thus it is not exact. So B3LYP is a functional constructed from a series of errors, B88 functional is fundamentally wrong, LYP is wrong, and the mixing is wrong, normally B3LYP should not exist, and it is a misunderstanding. B3PW91 is properly constructed and it is better in many areas, e.g. for larger molecules.
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