# Suggest methods and basis sets for a variety of systems

Please help me with any/all of the cases below. In the following cases, the named method and basis set are not suitable for the chemical systems. Why aren't they? Could you suggest a suitable method/basis set for each?

### 1. MP2/6-31G(d) for the calculation of reaction energy of the reaction below (H2C: should be calculated in the triplet state):

The carbene H2C: has two singlet configurations that contribute to the ground state energy, so we need a multireference method to recover the single excitations. MP2 is not good for this open-shell systems since they have large spin contamination and thus large error. The basis set also needs to include diffuse functions for electron correlation methods.

### 2. CISD/cc-pVTZ for the calculation of the reaction energy of:

We have bond elongation in the reactant to the point of breakage. CISD is not size-consistent. It recovers less electron correlation energy for the larger reactant than for the products since the reactant is larger, so CISD cannot be used. The basis set however is fine. I don't know what method can work best for this system but would go arbitrarily with CCSD(T).

### 3. BLYP/6-31G(d) for geometry optimization and calculation of binding energy of the neon dimer, $\ce{Ne\bond{...}Ne}$.

The most important interactions in the Ne dimer are London forces, or van der Waals (vdW) interactions. BLYP is a hybrid DFT method that includes exact exchange term in exchange-correlation functional. However, the method is local (in LDA, the external potential is the uniform electron gas, and in a GGA, its gradient is included), and vdW interaction requires fully non-local functionals. The basis set is also too small and should include diffuse functions. I don't know what method to recommend.

### 4. MP2/6-311++G(2df,p) for the singlet-triplet energy splitting of para-benzyne. Note that for both singlet and triplet states unrestricted MP2 is needed.

The para-related electrons have low correlation, meaning they have small singlet-triplet separations of the frontier orbitals. MPn energy terms are related to the inverse of this separation and thus for a very small s-t separation, this term is too large for MP2 to handle. The basis set is probably fine. I think coupled cluster methods or DFT would work here.

### 5. CCSD/3-21G for geometry optimization of the DNA base adenine.

The basis set is too small for this molecule and a correlated method (no diffuse or polarization functions are used). Furthermore, CCSD is very costly and not good for this big molecule. Maybe handling the conjugated pi bonds is important. Suggestions?

### 6. CISD/6-311G(d,p) to compare the CC bond lengths of oligoenes ($2<n<20$).

CISD is not size-extensive, so as $n$ increases, the calculations become prohibitive.

### 7. MP3/6-311G(d,p) for the electron affinity of F2 i.e. the process:

MP3 is not good when we have an open-shell species or a system with electron congestion. Convergence will be very slow and not guaranteed at all. We assume in MPn that the zeroth-order wavefunction is a reasonable approximation, and the electron correlation contribution can be added as a small perturbation. But if HF describes this molecule very poorly, then MPn won't improve upon the zeroth-order wavefunction dramatically.

### 8. LSDA/6-31G(d) for the relative energies of the various conformations of n-butane obtained through rotation about the central C-C bond.

LSDA is equal to LDA for closed shell systems. Thus the external potential is the uniformly distributed positive charge and can be used only if the "constant" electron density is different for each point in space. However, here the electron density due to bond twisting is not spatially uniform. I think a GGA or B3LYP should be used. Furthermore, I think the basis set is too small and should include extra polarization and diffuse functions (I don't know why, just saying).

## What method/basis set would you suggest for the following:

### 9. The activation energy of the Diels-Alder reaction between cyclopentadiene and acrylonitrile (reaction does not need static electron correlation treatment).

Pure LDAs or GGAs overestimate bond length, so I suggest the hybrid B3LYP with a small basis set.

### 10. The interaction energy between two Ar atoms in the $\ce{Ar\bond{...}Ar}$ van der Waals complex.

Use CCSD with a medium basis set, since vdW is repulsion of electron clouds at large distances as they interpenetrate and CCSD has traces of higher excitations. A small basis set can cause basis set superposition error (BSSE). Inclusion of higher order virtual orbitals as in CCSD improves the dispersion description.

• Is this a homework question? Post your attempts at answering each point and we can try to help you from there. – LordStryker Jan 20 '14 at 18:50
• @AliRaf: BLYP is not the same as B3LYP -- B3LYP is a hybrid functional, while BLYP is a GGA. For (v) I'd just use a hybrid functional of some sort: B3LYP should do a perfectly adequate job. For (iii) I'd want something with excitations but I'd want to use something different for the initial geometry optimisation and then something expensive for the energy calculation, maybe at a few different points to verify the geometry. – Aesin Jan 20 '14 at 20:06
• For Problem 9, just because a method doesn't calculate the geometry well doesn't meant the energetics will be inaccurate. There is often not a huge correlation between accurate geometries and accurate energies, unfortunately. B3LYP is commonly used for reaction energetics of organics. The M06 suite of functionals is parameterized for thermochemistry, so that could be a good (more modern) choice. – Argon Mar 18 '18 at 3:21

This is a great question and I love it. Thank you for taking the time to not only post the question but each attempted response. I will try to address the parts of this question that I can at the moment. I will list, in order, your attempted answer along with my response.

1. Carbene H2C: has two singlet configurations that contribute to the ground state energy we need a multireference method to recover the single excitations. MP2 is not good for this open-shell systems since they have large spin contamination and thus large error. The basis set also needs to include diffuse functions in the electron correlation methods.

Yes, a multireference method will need to be used and a complete active space will need to be defined. Therefore, MP2 will NOT work. The 6-31(d) basis set is atrocious and should never be used for production level work given the growth of computing power in the last decade. This double-$\zeta$ quality basis set is much too small and at minimum a triple-$\zeta$ basis set should be used. Diffuse functions are critical to properly describe the spatial electronic region of a weakly bound electron far away from the nucleus, but in this case, I would only include diffuse functions on non-hydrogen atoms given that the unpaired electrons are on carbon and not hydrogen (as per your picture). Lastly, polarization functions should be included on every atom, and not just the non-hydrogen atoms. Therefore I would use a basis set such as 6-311+G(d,p), 6-311+G(2df,2pd), or even heavy-aug-cc-pVTZ. Quadruple-$\zeta$ basis sets should be used if you can afford it but may not be feasible in this case.

1. We have bond elongation in the Reactant to the point of breackage. CISD is not size-consistent. It recovers less electron correlation energy for the larger reactant as for the products since reactant is larger and thus cannot be used. The basis set however is fine. I don't know what method can work best for this system but would go arbitrarily with CCSD(T).

CISD does introduce size-consistency problems but there are 'workarounds' you can use (example). Obviously we want to avoid using more and more approximations so it would be prudent to avoid CISD in this case. The basis set could be dramatically improved by adding diffuse functions to the non-hydrogen atoms (e.g. heavy-aug-cc-pVTZ).

1. Most important interactions in Ne dimer are London forces of van der Waals. BLYP is a hybrid DFT method that includes exact exchange term in exchange-correlation functional. However, the method is local (in LDA, external potential is the uniform electron gas and in GGA its gradients included) but vdW interaction requires fully non-local functionals. The basis set is as well too small and should included diffuse functions. I don't know what method to recommend.

The neon dimer is a very interesting system. How does two atoms with full valency (8 electrons) bind? This is where electron correlation comes into play. It is due to the correlated motions of the electrons that allow these two atoms to form a bond, albeit a very, very weak bond. This is known as non-covalent interactions or dispersion interactions. For these types of systems, very expensive correlated methods are absolutely required to get it right. DFT methods fail at properly describing dispersion forces though a lot of advancements have been made to build in a dispersion correction to the canonical functionals. These corrections are usually denoted as -DX, where X is the generation of that correction (currently we are on -D3, or the 3rd generation of these types of corrections). BLYP has no dispersion corrections built in and therefore will likely tell you that the neon dimer is UNBOUND (i.e. the binding energy is positive at all interatomic separations). Unsurprising. Therefore you will have to use a correlated method such as MP2. But even MP2 can do a poor job of describing dispersion interactions (example). In this example, MP2 overbinds the PCCP dimer by as much as 5 kcal mol$^{-1}$ with respect to CCSD(T). CCSD(T) is what we generally consider to be the correct answer. Given that CCSD(T) binds the PCCP dimer by only 1-2 kcal mol$^{-1}$, you can see the problem here. The error of the MP2 method is about 5 times as large as the actual binding energy, and that is a major problem. The basis set is also too small and you MUST include diffuse functions on both Neon atoms. Without these diffuse functions, even correlated methods will have a hard time determining if this thing actually binds at all.

1. The basis set is too small for this molecule and a correlated method (no diffuse or polarization functions are used). Furthermore, CCSD is very costly and not good for this big molecule. Maybe also conjugated pi bonds is of essence. Suggestion?

The question deliberately states 'optimization'. Therefore, nearly any commonly used density functional could be used (e.g. B3LYP). If you want a slightly better result, go for some newer functionals such as the Minnesota functionals from Truhlar's group (e.g. M06-2X, M08-2X, etc.) or try some dispersion-corrected functionals. If the question asked what you would use to determine the energetics, THEN move on to something like MP2 or CCSD(T). I wouldn't trust the DFT energetics unless they have been extensively calibrated in previous work. (Protip: never rely on DFT methods which haven't be calibrated for your type of system... in fact, just don't trust DFT at all :P). The basis set is much too small. A DFT optimization will go quick enough that a triple-$\zeta$ basis set should be used. It goes without saying that you should include polarization functions on ALL atoms and diffuse functions on the non-hydrogen atoms (e.g. heavy-aug-cc-pVTZ, 6-311+G(2df,2pd), etc.).

1. CISD is not size-extensive so as n increases the calculations become prohibitive.

To be honest, I have a hard time coming up with an answer to this as the "question" is not very clear as to what the goal is.

1. MP3 is not good when we have an open-shell species or a system with electron congestion. Convergence will be very slow and not guaranteed at all. We assume in MPn that the zeroeth order wavefunction is reasonable approximation and the add the small perturbation contribution. But if HF describes this molecule very poorly then MPn won't improve it dramatically.

Yes, MP3 is not guaranteed to converge at all which is pretty much the only reason (in my opinion) that you should need. By the time you figure out the convergence/divergence/oscillation of the MPn series, you would have been better off sticking to something that is more expensive but guaranteed to converge. Stick to CC methods.

1. LSDA is equal to LDA for closed shell systems. Thus eternal potential is the uniformly distributed positive charge and can be used only if the "constant" electron density is different for each point in space. But here electron density due to bond twisting is not spatially uniform. I think GGA or B3LYP should be used. Furthermore I think the basis set is too small and should include polarization and diffusion (I don't know why, just saying).

Given the fact that we've come a long way since LSDA, any use of LSDA for any type of production level work should just downright be avoided. Here I would use GGAs or meta-GGAs. They are much better. Also, a larger basis set should be used. (polarization functions for all atoms, diffuse on non-hydrogen atoms, blah blah blah).

1. pure LDA or GGA overestimate bond length so I suggest hybrid B3LYP with small basis set

This question deliberately asks how you would go about determining the activation ENERGY of this reaction. Therefore, do NOT rely on any DFT method when it comes to energetics UNLESS extensive calibration has been done. Here's what I would do for this if I were going to turn this into a research paper. First and foremost, optimize these guys with MP2/heavy-aug-cc-pVTZ. They are small enough that this could be done. Now, if I wanted to use DFT, I would pick a slew of DFT methods of various flavors including hybrids, dispersion-corrected, etc. and optimize each geometry as well. Now, for each MP2 optimized geometry, I would do some high level single point energy computations using explicitly correlated methods such as MP2-F12 AND CCSD(T)-F12. (The explicitly correlated methods accelerate the convergence of the correlation to the CBS limit over canonical implementations. Essentially, MP2-F12/haTZ energetics can be on par with MP2/ha5Z energetics. Same goes for CCSD(T).) Given the size of these systems, I would (at the very least) bust out Dunning's correlation-consistent series of basis sets and push them as far as I could go. From eyeballing the system, I think I could get away with doing heavy-aug-cc-pVDZ and heavy-aug-cc-pVTZ right off the bat. I'm pretty sure I could do heavy-aug-cc-pVQZ as well. Once I've done this, I have a darn good idea how close to the CBS limit my energetics are. Now I can compare the DFT binding energies to the 'right answer' and boom, I've got DFT results I can rely on. Of course, if the MP2 and CCSD(T) energetics show significant deviation, then we would have to revisit our optimization procedures but I don't think it would be an issue in this case.

1. CCSD with medium basis set. Since vdW is repulsion of electron clouds at large distances as they interpenetrate and CCSD has traces of higher excitations. A small basis set can cause basis set superposition error (BSSE). Inclusion of higher order virtual orbitals as in CCSD improves dispersion description.

I would not recommend CCSD. You might as well do an MP2 calculation to be honest but for this type of system with a large dispersion component, you will want to do CCSD(T) energetics. System is small enough to use a quadruple-$\zeta$ quality basis set. Add diffuse and polarization functions. Also, the frozen-core approximation should be tested. You may want to correlate ALL the electrons to determine core-core and core-valence electron effects (use something like aug-cc-pCVQZ).