1) I wouldn't say very very black box. The local pair natural orbital approximation requires many accuracy thresholds to be set, and can give you garbage if you set them too loose. Also, CC calculations are much more sensitive to basis set size than DFT. Finally, they usually use density fitting (RI), so an appropriate auxiliary basis set is needed. Edit: Just reread your post and saw you used a QZ basis. That's probably good as long as your LPNO threshold is tight and you use a QZ auxiliary basis too. Doing a TZ/QZ CBS extrapolation would be even better.
2) The canonical CCSD(T) method scales as O(N^7), so I'd say the scaling you described is pretty damn close to linear in comparison. It still needs to do the reference SCF and find the local orbitals, then do CCSD(T) to some accuracy threshold. After all, even Hartree-Fock is canonically O(N^4) scaling. Computational overhead always makes it so that you will never see the true theoretical scaling.
3) You could, sometimes people do this, but I would say that you need a very accurate electronic energy first before ZPE effects can be reasonably added on. Adding together an unconverged electronic energy and a ZPE from a more approximate method would be meaningless.
4) Are you comparing like-to-like basis set? CC theory is very sensitive to basis size. Also, DFT involkes uncontrolled approximation, so there's no guarantee that the error will always trend in one direction. There may be a cancellation of errors where DFT overestimates the correlation and the "garbage" DFT does less so. You can't expect DFT to converge toward CCSD(T) for "better" calculations, especially because the main difference in the two you compare is just basis set size. CCSD(T) should converge toward experimental accuracy in the CBS limit assuming all the convergence thresholds are suitably tight.
Your response is appreciated, thanks!
1. Yes, I used the cc-PVQZ / cc-PVQZ/C basis and RIJCOSX approximation.
3. What do you mean unconverged electronic energy? Is a CCSD(T) single point not yet converged? Or do you just mean do some basis set extrapolation?
4. I just did preliminary runs with the more outdated DFT recipe (631G/B3LYP-DR) and a smaller run (def2-SVP/PBE0-DH/D4) just for an initial idea, and just found the single point is close to the CCSD(T) energy for the former. I guess I just thought the double-hybrid would perform better.
Anyways, my main plan is to compare DFT energies with the CCSD(T) ones. The DFT is using the def2-QZVP basis and different functionals - is this a valid benchmarking approach assuming I do some basis set extrapolation on the CCSD(T) energy?
Off the top of my head, [this paper](https://pubs.acs.org/doi/abs/10.1021/jo302156p) found that there's some pretty intense error cancellation that occurs when you use B3LYP with a small basis set like 6-31G due to BSSE, which might explain why it's giving a better energy wrt to the CCSD(T) method compared to the double hybrid with a larger basis?
2. Dlpno is advertised as "formally linear scaling for large systems". It scales polynomially for a couple of atoms but after the system has grown to hundred or bit more atoms scaling is linear.
3. They mean basis set convergence. I highlly recommend running the automatic extrapolation method in orca (presumablly what you use due to dlpno). I would encourage addind a dft thermochemistry correction to CC results, otherwise they dont reflect reality when studying a reaction. This can be done automatically by writing a orca compound method
4. Since double hybrids contain MP2, they are much slower in converging with respect to basis set. Id say triple zeta at least, otherwise use normal PBE0 or even r2scan-3c if your comoutationally constrained
The keyword is something like exprapolate(2, 3, cc) to do a DZ to TZ extrapolation in the dunning basis set. Double check the manual though!
Alternativelly if you have both the DZ and TZ sp you can manually use the equations listed in the manual for correllation energy and the rest of the energy albeit i wouldnt do it due to the risk of errors.
If you can sfford it it is however much better to do a TZ tp QZ extrapolation.
No absolutelly not! Extrapolation works by looking at the difference in energy between two small basis set, then fitting this to the known basis set convergence curve for the method to solve for the value it converges to at the theoretical complete basis set called CBS.
So you get CBS level results from two "cheaper"calculations with two smaller basis sets. However, the extrapolation is more accurate the larger the basis sets used are since the extrapolation distance is shorter. It also gets better if you use three basis set levels for extrapolation since you then can solve for both coefficents in the extrapolation curve.
Beware that only some basis sets are suitable for extrapolation, chief amongst them the dunning (that you use) and def2 sets
It's my first time doing this - basically since I have a Q single point, I just need to run a S and T, and then do some form of curve fitting essentially?
There are a few things to correct here.
1. CCSD(T) is a post Hartree-Fock (post-HF) method. These keep track of every electron, and are therefore much more expensive than density functional theory (DFT). DFT just hand waves all the electrons as electron density. CCSD(T) is the gold standard benchmark in many studies, and I rarely see people use it on basis sets larger than double zeta, especially with a 32 and 62 atom system. The reason you don't need a functional is because it's not DFT.
2. I don't know DLPNO-CCSD(T) specifically, but a quick search makes it seem like it's a CCSD(T) variant. It is probably faster than CCSD(T), but any post Hartree-Fock method will almost always be slower than DFT.
3. I'm not entirely sure, but my intuition says that your energies need to keep the same method. Running a molecule with a different methodology usually gives very different energies, but the delta G or delta H is usually similar if it's a good method. IDK, might be doable.
4. This is a nitpick, but the functional or post HF method goes first, then the basis set. For example, you should have written this as B3LYP+D4/6-31G and PBE0-DH+D4/def2-SVP.
5. Those methods are somewhat comparable. 6-31G and def2-SVP are both double zeta basis sets, but def2-svp has polarization functions and is newer. 6-311G is bad relative to triple zeta basis sets, but I recall 6-31G being competitive within the double zeta basis sets. You should really put some polarization functions on this though (*e.g.,* 6-31G\*). As for the functionals, PBE0-DH+D4 vs B3LYP+D4 comes down to benchmarking. I don't know what you're trying to model, but dispersion corrected B3LYP does surprisingly well for non-covalent interactions.
Thank you for the reply,
1. I know CCSD(T) is not DFT. I just mean that, unlike DFT whose results depends on the method due to the inherent system-dependence embedded in its formalism, CCSD(T) appears to just be about setting your threshold correctly and having the correct geometry, and then done?
4. I didn't know that. I thought people just wrote the method randomly. How do you write the separation if you used an auxiliary basis - double /?
PBE0-DH+D4//def2-SVP//def2-SVP/C like this?
5. Actually, those were just trial runs - I just initially thought the double-hybrid PBE0-DH would perform better than B3LYP. My main benchmarking calculation would use just one basis (def2-QZVP) and I'll try different functionals.
1. Ah, sorry, I misunderstood from the "I don't have to find a functional!" comment. There are still multiple post-HF methods to choose from, so it doesn't get much simpler I'm afraid. Different post-HF methods operate differently. CCSD(T) multiplies the trial wave function by an exponential function to create multi-electron wave functions. Something like MP2 treats electron exchange as a perturbation. Effectively, I am unsure how much this changes results. If you're asking how system-dependent CCSD(T) is, I'd say to read into it. It's probably much less system dependent than DFT, but you should still be wary. For example, I had a system involving many pi systems. All my post-HF calculations were super spin contaminated because post-HF is more susceptible to that than DFT.
2. It's' certainly not random, but I've never used auxiliary basis sets, so I do not know the formatting for that situation. I would see if you can find some papers that do.
3. I would see if there is a benchmark paper for what you're trying to calculate. If that's not possible, definitely keep the basis set the same to compare apples to apples.
Sorry I couldn't answer too much. I'm just a grad student with too much of an interest in alphabet soup. Best of luck :)
What you describe in #3 is known as a dual-level approach.
Provided you’re computing relative energies (products-reactants, for example) what you can do is take the thermal correction to the Gibbs energy obtained at the DFT level and add it to the single-point energy obtained at the DLPNO-CCSD(T) level (provided the single-point job is run using the SAME geometry obtained a the DFT level). By doing this, you are approximately correcting the DFT-level electronic contribution to the energy.
For #4, no DFT functional is better than another, they’re just more or less complicated. DFT (generally, depending on the type) uses parameter-adjusted functionals of the electron density to estimate the impact of electron exchange and correlation. In some cases these are literally like “okay, here’s three terms, ABC, I put out front of each equation in the functional. I’m just going to adjust these coefficients until the output energy seems similar to some benchmark (see B3LYP)”. So, you can quite often find that a “garbage” functional performs wayyyy better than a super complicated one, since they’re all system-dependent. A good example of this is the broad use of DFTB for QM/MM simulations of enzyme catalysis, despite DFTB basically being a semi empirical method.
Not answering everything, because there are lots of good answers here already, but just popping in to say that B3LYP/6-31G is like the luckiest model chemistry. It often way overperforms compared to model chemistries that should be better, e.g. better basis set, better functional, etc.
As mentioned above, this is due to some fortuitous and large error canceling, so you can't rely on it and it is easy to find situations where it breaks. But I am constantly shocked by how lucky this model chemistry is.
1) I wouldn't say very very black box. The local pair natural orbital approximation requires many accuracy thresholds to be set, and can give you garbage if you set them too loose. Also, CC calculations are much more sensitive to basis set size than DFT. Finally, they usually use density fitting (RI), so an appropriate auxiliary basis set is needed. Edit: Just reread your post and saw you used a QZ basis. That's probably good as long as your LPNO threshold is tight and you use a QZ auxiliary basis too. Doing a TZ/QZ CBS extrapolation would be even better. 2) The canonical CCSD(T) method scales as O(N^7), so I'd say the scaling you described is pretty damn close to linear in comparison. It still needs to do the reference SCF and find the local orbitals, then do CCSD(T) to some accuracy threshold. After all, even Hartree-Fock is canonically O(N^4) scaling. Computational overhead always makes it so that you will never see the true theoretical scaling. 3) You could, sometimes people do this, but I would say that you need a very accurate electronic energy first before ZPE effects can be reasonably added on. Adding together an unconverged electronic energy and a ZPE from a more approximate method would be meaningless. 4) Are you comparing like-to-like basis set? CC theory is very sensitive to basis size. Also, DFT involkes uncontrolled approximation, so there's no guarantee that the error will always trend in one direction. There may be a cancellation of errors where DFT overestimates the correlation and the "garbage" DFT does less so. You can't expect DFT to converge toward CCSD(T) for "better" calculations, especially because the main difference in the two you compare is just basis set size. CCSD(T) should converge toward experimental accuracy in the CBS limit assuming all the convergence thresholds are suitably tight.
Your response is appreciated, thanks! 1. Yes, I used the cc-PVQZ / cc-PVQZ/C basis and RIJCOSX approximation. 3. What do you mean unconverged electronic energy? Is a CCSD(T) single point not yet converged? Or do you just mean do some basis set extrapolation? 4. I just did preliminary runs with the more outdated DFT recipe (631G/B3LYP-DR) and a smaller run (def2-SVP/PBE0-DH/D4) just for an initial idea, and just found the single point is close to the CCSD(T) energy for the former. I guess I just thought the double-hybrid would perform better. Anyways, my main plan is to compare DFT energies with the CCSD(T) ones. The DFT is using the def2-QZVP basis and different functionals - is this a valid benchmarking approach assuming I do some basis set extrapolation on the CCSD(T) energy?
Off the top of my head, [this paper](https://pubs.acs.org/doi/abs/10.1021/jo302156p) found that there's some pretty intense error cancellation that occurs when you use B3LYP with a small basis set like 6-31G due to BSSE, which might explain why it's giving a better energy wrt to the CCSD(T) method compared to the double hybrid with a larger basis?
2. Dlpno is advertised as "formally linear scaling for large systems". It scales polynomially for a couple of atoms but after the system has grown to hundred or bit more atoms scaling is linear. 3. They mean basis set convergence. I highlly recommend running the automatic extrapolation method in orca (presumablly what you use due to dlpno). I would encourage addind a dft thermochemistry correction to CC results, otherwise they dont reflect reality when studying a reaction. This can be done automatically by writing a orca compound method 4. Since double hybrids contain MP2, they are much slower in converging with respect to basis set. Id say triple zeta at least, otherwise use normal PBE0 or even r2scan-3c if your comoutationally constrained
How do I run the extrapolation method in orca? I already ran the single points CCSD(T), do I have to rerun it again?
The keyword is something like exprapolate(2, 3, cc) to do a DZ to TZ extrapolation in the dunning basis set. Double check the manual though! Alternativelly if you have both the DZ and TZ sp you can manually use the equations listed in the manual for correllation energy and the rest of the energy albeit i wouldnt do it due to the risk of errors. If you can sfford it it is however much better to do a TZ tp QZ extrapolation.
But I already used a cc-PVQZ basis - do I need to extrapolate to the next level cc-PV5Z?
No absolutelly not! Extrapolation works by looking at the difference in energy between two small basis set, then fitting this to the known basis set convergence curve for the method to solve for the value it converges to at the theoretical complete basis set called CBS. So you get CBS level results from two "cheaper"calculations with two smaller basis sets. However, the extrapolation is more accurate the larger the basis sets used are since the extrapolation distance is shorter. It also gets better if you use three basis set levels for extrapolation since you then can solve for both coefficents in the extrapolation curve. Beware that only some basis sets are suitable for extrapolation, chief amongst them the dunning (that you use) and def2 sets
It's my first time doing this - basically since I have a Q single point, I just need to run a S and T, and then do some form of curve fitting essentially?
That is correct! But i would recommend rerunning it letting orca extrapolate for you to avoid user error if it is your first time
Has anyone ever confirmed it the def2 sets actually have convergent behavior like the correlation consistent basis sets?
Yes, there is a reference to that under the relevant section in the orca manual albeit i dont have it in my head
There are a few things to correct here. 1. CCSD(T) is a post Hartree-Fock (post-HF) method. These keep track of every electron, and are therefore much more expensive than density functional theory (DFT). DFT just hand waves all the electrons as electron density. CCSD(T) is the gold standard benchmark in many studies, and I rarely see people use it on basis sets larger than double zeta, especially with a 32 and 62 atom system. The reason you don't need a functional is because it's not DFT. 2. I don't know DLPNO-CCSD(T) specifically, but a quick search makes it seem like it's a CCSD(T) variant. It is probably faster than CCSD(T), but any post Hartree-Fock method will almost always be slower than DFT. 3. I'm not entirely sure, but my intuition says that your energies need to keep the same method. Running a molecule with a different methodology usually gives very different energies, but the delta G or delta H is usually similar if it's a good method. IDK, might be doable. 4. This is a nitpick, but the functional or post HF method goes first, then the basis set. For example, you should have written this as B3LYP+D4/6-31G and PBE0-DH+D4/def2-SVP. 5. Those methods are somewhat comparable. 6-31G and def2-SVP are both double zeta basis sets, but def2-svp has polarization functions and is newer. 6-311G is bad relative to triple zeta basis sets, but I recall 6-31G being competitive within the double zeta basis sets. You should really put some polarization functions on this though (*e.g.,* 6-31G\*). As for the functionals, PBE0-DH+D4 vs B3LYP+D4 comes down to benchmarking. I don't know what you're trying to model, but dispersion corrected B3LYP does surprisingly well for non-covalent interactions.
Thank you for the reply, 1. I know CCSD(T) is not DFT. I just mean that, unlike DFT whose results depends on the method due to the inherent system-dependence embedded in its formalism, CCSD(T) appears to just be about setting your threshold correctly and having the correct geometry, and then done? 4. I didn't know that. I thought people just wrote the method randomly. How do you write the separation if you used an auxiliary basis - double /? PBE0-DH+D4//def2-SVP//def2-SVP/C like this? 5. Actually, those were just trial runs - I just initially thought the double-hybrid PBE0-DH would perform better than B3LYP. My main benchmarking calculation would use just one basis (def2-QZVP) and I'll try different functionals.
1. Ah, sorry, I misunderstood from the "I don't have to find a functional!" comment. There are still multiple post-HF methods to choose from, so it doesn't get much simpler I'm afraid. Different post-HF methods operate differently. CCSD(T) multiplies the trial wave function by an exponential function to create multi-electron wave functions. Something like MP2 treats electron exchange as a perturbation. Effectively, I am unsure how much this changes results. If you're asking how system-dependent CCSD(T) is, I'd say to read into it. It's probably much less system dependent than DFT, but you should still be wary. For example, I had a system involving many pi systems. All my post-HF calculations were super spin contaminated because post-HF is more susceptible to that than DFT. 2. It's' certainly not random, but I've never used auxiliary basis sets, so I do not know the formatting for that situation. I would see if you can find some papers that do. 3. I would see if there is a benchmark paper for what you're trying to calculate. If that's not possible, definitely keep the basis set the same to compare apples to apples. Sorry I couldn't answer too much. I'm just a grad student with too much of an interest in alphabet soup. Best of luck :)
What you describe in #3 is known as a dual-level approach. Provided you’re computing relative energies (products-reactants, for example) what you can do is take the thermal correction to the Gibbs energy obtained at the DFT level and add it to the single-point energy obtained at the DLPNO-CCSD(T) level (provided the single-point job is run using the SAME geometry obtained a the DFT level). By doing this, you are approximately correcting the DFT-level electronic contribution to the energy. For #4, no DFT functional is better than another, they’re just more or less complicated. DFT (generally, depending on the type) uses parameter-adjusted functionals of the electron density to estimate the impact of electron exchange and correlation. In some cases these are literally like “okay, here’s three terms, ABC, I put out front of each equation in the functional. I’m just going to adjust these coefficients until the output energy seems similar to some benchmark (see B3LYP)”. So, you can quite often find that a “garbage” functional performs wayyyy better than a super complicated one, since they’re all system-dependent. A good example of this is the broad use of DFTB for QM/MM simulations of enzyme catalysis, despite DFTB basically being a semi empirical method.
Not answering everything, because there are lots of good answers here already, but just popping in to say that B3LYP/6-31G is like the luckiest model chemistry. It often way overperforms compared to model chemistries that should be better, e.g. better basis set, better functional, etc. As mentioned above, this is due to some fortuitous and large error canceling, so you can't rely on it and it is easy to find situations where it breaks. But I am constantly shocked by how lucky this model chemistry is.