# Is this statement about the SAPT analysis true?

Dear friends,
Some researchers argue that:
" In the SAPT approach the magnitude of perturbative Hamiltonian operator (V_ inter) corresponding to intermolecular interaction should essentially be small compared to chemical bonding interaction; otherwise, the applicability of SAPT may become somewhat controversial. Indeed, as the strength of an HB interaction increases, the degree of charge transfer as well as orbital interactions between two monomers are also increased, leading to an increase in the extent of (V_ inter), thereby the accuracy of the resulted SAPT-derived BE value is expected to more deviates from that obtained through high-level supermolecular approach.
Please let me know how much such statement is reliable about dependence between applicability of SAPT and the magnitude of perturbation in the considered system.

Best regards,
Saeed

Hi Saeed,
I wholeheartedly agree with almost all of statement you’ve quoted. It is certainly true that for any perturbative approach (including MBPT, SAPT, etc.), if the perturbation is too large, the assumptions the theory is based upon break down. That’s why it’s not possible to simply apply perturbation theory to account for missing static correlation in Hartree–Fock for bond cleavage processes—the perturbation is just too large for any such theory to be valid.

In the quote, you specifically mention hydrogen bonding:

Typically, hydrogen bonding events don’t constitute a sufficiently large interaction that SAPT is vulnerable to this sort of problem, however. Even for the binding energies of doubly hydrogen bound dimers constructed from combinations of formic acid, formamide, and and formamidine (which exhibit binding energies of up to -25 kcal/mol), SAPT0 still compares favorably to supramolecular CCSD(T) benchmarks. It may be important to employ exchange scaling approaches (e.g., sSAPT0, see here for an explanation) in these contexts, but you shouldn’t be afraid of applying SAPT0 to even hydrogen bonding interactions as long as the structure you’re looking at isn’t in the middle of a proton transfer.

That being said, however, it is possible to apply SAPT0 (and especially sSAPT0) to study noncovalent interactions in transition state complexes (see, e.g, here and here) as long as it’s done super carefully. For transition states, where the interaction strength between fragments might be as large as -100 kcal/mol or more, you’d definitely need to validate the SAPT energetics against CCSD(T) or some other benchmark on a case-by-case basis to be safe.

Hope that helps!

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Dear Dasirianni,
Too many thanks for your so nice, informative and comprehensive explanations. Your kindly attention to introduce some interesting articles is highly appreciated as well.
Considering your comments, seemingly, we are allowed to employ different SAPT levels to analyze different interactions with various strength as this approach has been used even for Carbene-BX3 interactions whose interaction energy was to be around 100 kcal/mol (J Mol Model (2012) 18:2003–2011). Please kindly let me know your valuable opinion and also let me know why you especially emphasize just on SAPT0 or sSAPT0.

Sincerely yours,
Saeed

Saeed –

The reason I’ve emphasized SAPT0 is due to original point you raised about the perturbation being too large. For SAPT0, there is only a second-order dependence on the intermolecular perturbation V — which is a bit like depending on V^2. For higher-order SAPT methods [e.g., SAPT2+, SAPT2+(3)], however, there are terms which have a higher-order dependence on V that behave more like V^3. So, the higher order terms are more sensitive to the perturbation strength, and thus dthese higher-order terms (and consequently their SAPT levels) become unreliable long before SAPT0.

For some technical reasons, even when the perturbation becomes slightly too large for SAPT0 to be reliable, using the exchange-scaling trick employed in sSAPT0 can “fix” the problem. That’s why I’ve particularly emphasized sSAPT0 — it will be the most reliable for large interaction strengths out of all SAPT methods, but again it should be trusted only on a case-by-case basis with the caveat that it must be validated against some benchmark like CCSD(T).

~DS

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Dear Dom,

Many thanks for your kindly attention to guide me so patiently with much valuable and informative comments.
It may be of worth to indicate that I am a Gaussian user (for years) and have been familiarized with so nice and powerful PSI4 code very recently (less than a month) to perform very informative SAPT analysis.

While I could deeply understand why you are emphasizing on sSAPT0, I am a bit confused! Now, in order to avoid any confusing and take your quite straightforward response, I am going to explain a simple example:
Suppose that the binding energy (BE) associated with hydrogen bond (HB) interaction in the negatively charged Cl…H…Cl system calculated at CCSD(T)/jul-cc-pVTZ level (including BSSE correction) to be -42.70 kcal/mol. Also, the employed supermolecular approach does not include deformation energy. Such a large BE value evidently indicates a large degree of perturbation in V_interaction and, hence, the results of respective SAPT analysis may be taken into question. Value of sSAPT0 and SAPT2+(3)/dMP2 (as the Gold level regarding such analyses) obtained employing aug-cc-pVTZ basis is -40.47 and -43.98 kcal/mol, respectively. So, since value of both sSAPT0 andSAPT2+(3)/dMP2, particularly the former based on you comments, is in excellent agreement with that of CCSD(T) one can definitely conclude that in the case under study the degree of perturbation is allowed to be considered not so large such that SAPT is still valid to be employed.

I would be much grateful if you kindly let me SIMPLY know your valuable opinion.

Sincerely,
Saeed

Saeed –

In the context of the example you’ve provided, both sSAPT0 and SAPT2+(3)+dMP2 seem to be generating reliable interaction energies, since the interaction energies are within 5% and 3% of the CCSD(T) result…so in short, yes, it looks promising!

That being said, I’d strongly suggest using a different level of theory for the coupled cluster benchmark, if you can afford it. CCSD(T) (and other electron correlation methods) converge very slowly with respect to basis set size – with CCSD(T)/aug-cc-pVDZ single point interaction energies falling short of reference values by nearly 1 kcal/mol in some cases – so the larger the basis set the better. If you can afford CCSD(T)/jun-cc-pVDZ, I’d suggest you use a composite complete-basis set approach combining MP2 and CCSD(T) (like the approach defined here) with the slight change that the basis set for the \delta correction be aug-cc-pVDZ instead of aug-cc-pVTZ.

You can request this energy approach in a Psi4 input file with the following:

energy('mp2/aug-cc-pv[t,q]z + d:ccsd(t)/aug-cc-pvdz')


Using this approach has been shown to be able to accurately reproduce interaction energies to within +/- 0.05 kcal/mol of high-level reference values, and it shouldn’t be much more expensive than the CCSD(T)/jun-cc-pVDZ you’ve already computed.

~ DS

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Dear Dom,

Too many thanks for your much valuable confirmation about the validity of my statement.
While I will consider your nice suggestion about employing MP2 interaction enrgy, please be aware that for the mentioned negatively charged system, the CCSD(T)/CBS binding energy (extrapolated using aug-cc-pV[T,Q]Z scheme) becomes -43.49 kcal/mol. Indeed, toward extrapolation, I have employed the following command line in PSI4:

energy(cbs,scf_wfn=‘scf’,scf_basis=‘aug-cc pV[TQ]Z’,scf_scheme=scf_xtpl_karton_2,corl_wfn=‘ccsd(t)’, corl_basis=‘aug-cc-pv[TQ]z’,bsse_type=[‘cp’,‘nocp’],scf_alpha=5.79,corl_alpha=3.05)

It seems, your suggested level is also another scheme of extrapolation in PSI4. Is it true?
In addition, could you please let me know corresponding reference (article) for the high validity of MP2/aug-cc-pV[T,Q]Z+d:CCSD(T)/aug-cc-pVDZ?

Sincerely,
Saeed

Saeed –

Yes, my suggested method is another CBS approach available in Psi4. Since the value you’ve computed with CCSD(T)/aug-cc-pV[T,Q]Z is even higher quality than the level I’ve suggested, however, you don’t need to use CCSD(T)/jun-cc-pVDZ for the benchmarking. Furthermore, the interaction energy value you provide for CCSD(T)/aug-cc-pV[T,Q]Z supports the application of SAPT to this system even more, since it is even closer to your SAPT2+(3)+dMP2/aug-cc-pVTZ interaction energy.

For choosing methods to benchmark interaction energies with various levels of target accuracy and computational cost, I’d recommend a few papers out of the Sherrill group (organized chronologically):

Of course these aren’t the only relevant papers, but they’re a start. Happy digging!

~ DS

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Dear Dom,
Please let me to present my highest and deepest gratitude for your kindness to spend much valuable time and energy guiding me with highly important points. You resolved all my current problems in the best feasible manner.

I really hope I can benefit of your much valuable helps in future.

Yours sincerely,
Saeed

Just a note, but I would advice to avoid a DZ basis for the delta_cc correction. I have not found it reliable. (in line with the JCP 2011 paper mentioned above). Unless as a last resort, but it usually does not do ‘gold standard’ justice and probably requires error compensation with insufficient MP2/CBS.

Dear Holger,