Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. I. Triples expansions

Janus J. Eriksen, Devin A. Matthews, Poul Jørgensen, and Jürgen Gauss (2015)

Contributed by Jan Jensen

Figure 1: Normal distributions of the recoveries of (in percent (%), Figure 1a) and deviations from (in kcal/mol, Figure 1b) CCSDT–CCSD frozen-core/cc-pVTZ correlation energy differences for RHF, UHF, and ROHF references. (Taken from the paper)

This paper argues that we shouldn't expect the kind of accuracy we have come to expect from CCSD(T) for closed shell molecules, for open-shell molecules.  I have a slightly different take on the data.

But first it is fair to ask whether coupled-cluster is an appropriate standard for open shell systems in the first place because of spin-contamination (note there is also spin-contamination in ROHF- coupled-cluster).  If you get significantly different answers for UHF- and ROHF-based calculations it is not clear which one is the most reliable.

The first thing the paper shows - for 18 atoms and small open shell molecules - is that spin-contamination decreases by roughly an order of magnitude for each step in SCF > CCSD > CCSDT > CCSDTQ so that it is negligible for the latter.  For most of the molecules the spin-contamination is also negligible for CCSDT.  This is good to know.

The authors go on to show that CCSD(T) is a worse approximation for CCSDT for open shell systems (see Figure 1) and that CCSD(T) is always a worse approximation to CCSDTQ than CCSDT for open shell systems, in contrast to closed shell systems.  While that's true, the data also shows that the CCSDT correlation energy is closer to the CCSDTQ energy for open shell systems.  In fact the the mean error in CCSD(T) correlation energies relative to CCSDTQ is actually lower for open shell systems (0.80, 0.70, and 0.57 kcal/mol for RHF-, UHF-, and ROHF-based calculations).  So this is good news.

One note of caution in all of this is that the study uses cc-pVTZ (understandable as CCSDTQ calculations are performed). It remains to be seen whether the conclusions are true for the CBS.

On a related note Anacker, Tew, and Friedrich have recently presented an incremental scheme for estimating UHF-based CCSD(T) energies for larger systems.



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Seeking Extremes in Molecular Design: To What Extent May Two “Non-Bonded” Hydrogen Atoms be Squeezed in a Hydrocarbon?

Firouzi, R.; Shahbazian, S. ChemPhysChem 2016, 17, 51-54
Contributed by Steven Bachrach
Reposted from Computational Organic Chemistry with permission

Setting the record for the shortest non-bonded H^…H contact has become an active contest. Following on the report of a contact distance of only 1.47 Å that I blogged about here, Firouzi and Shahbazian propose a series of related cage molecules with C-H bonds pointed into their interior.¹ The compounds were optimized with a variety of computational methods, and many of them have H^…H distances well below that of the previous record. The shortest distance is found in 1, shown in Figure 1. The H^…H distance in 1 is predicted to be less than 1.2 Å with a variety of density functionals and moderate basis sets.

1

Figure 1. Optimized geometry of 1 at ωB97X-D/cc-pVDZ.

References

(1) Firouzi, R.; Shahbazian, S. "Seeking Extremes in Molecular Design: To What Extent May Two “Non-Bonded” Hydrogen Atoms be Squeezed in a Hydrocarbon?," ChemPhysChem 2016, 17, 51-54, DOI:10.1002/cphc.201501002.

InChIs

1: InChI=1S/C41H44/c1-7-13-25-17-9-3-40-5-11-19(35(17)40)27-15-8-2-39(1,33(13)15)34-14(7)26-18-10-4-41-6-12-20(36(18)41)28(16(8)34)32(27)30-23(11)37(40)21(9)29(31(25)26)22(10)38(41)24(12)30/h7-38H,1-6H2
InChIKey=DMWSEJFKSWCSLI-UHFFFAOYSA-N

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A Practicable Real-Space Measure and Visualization of Static Electron-Correlation Effects

Grimme, S.; Hansen, A. Angew. Chem. Int. Ed. 2015, 54, 12308-12313
Contributed by Steven Bachrach
Reposted from Computational Organic Chemistry with permission

Assessing when a molecular system might be subject to sizable static (non-dynamic) electron correlation, necessitating a multi-reference quantum mechanical treatment, is perhaps more art than science. In general one suspects that static correlation will be important when the frontier MO energy gap is small, but is there a way to get more guidance?

Grimme reports the use of fractional occupancy density (FOD) as a visualization tool to identify regions within molecules that demonstrate significant static electron correlation.¹ The method is based on the use of finite temperature DFT.^2,3

The resulting plots of the FOD for a series of test cases follow our notions of static correlation. Molecules, such as alkanes, simple aromatics, and concerted transition states show essentially no fractional orbital density. On the other hand, the FOD plot for ozone shows significant density spread over the entire molecule; the transition state for the cleavage of the terminal C-C bond in octane shows FOD at C₁ and C₂but not elsewhere; p-benzyne shows significant FOD at the two radical carbons, while the FOD is much smaller in m-benzyne and is negligible in o-benzyne.

This FOD method looks to be a simple tool for evaluating static correlation and is worth further testing.

References

(1) Grimme, S.; Hansen, A. "A Practicable Real-Space Measure and Visualization of Static Electron-Correlation Effects," Angew. Chem. Int. Ed. 2015, 54, 12308-12313, DOI: 10.1002/anie.201501887.

(2) Mermin, N. D. "Thermal Properties of the Inhomogeneous Electron Gas," Phys. Rev. 1965, 137, A1441-A1443, DOI: 10.1103/PhysRev.137.A1441.

(3) Chai, J.-D. "Density functional theory with fractional orbital occupations," J. Chem. Phys 2012, 136, 154104, DOI: doi: 10.1063/1.3703894.

[Editors note: this paper has also been highlighted by Tobias Schwabe]


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Enhancing NMR Prediction for Organic Compounds Using Molecular Dynamics

Kwan, E. E.; Liu, R. Y. J. Chem. Theor. Comput. 2015, 11, 5083-5089
Contributed by Steven Bachrach
Reposted from Computational Organic Chemistry with permission

The prediction of NMR chemical shifts and coupling constants through ab initio computation is a major development of the past decade in computational organic chemistry. I have written about many developments on this blog. An oft-used method is a linear scaling of the computed chemical shifts to match those of some test set. Kwan and Liu wondered if the dynamics of molecular motions might be why we need this correction.¹

They suggest that the chemical shift can be computed as

<σ> = σ(static molecule using high level computation) + error

where the error is the obtained by using a low level computation taking the difference between the chemical shifts obtained on a dynamic molecule less that obtained with a static molecule. The dynamic system is obtained by performing molecular dynamics of the molecule, following 25 trajectories and sampling every eighth point.

They find outstanding agreement for the proton chemical shift of 12 simple molecules (mean error of 0.02 ppm) and the carbon chemical shift of 19 simple molecules (mean error of 0.5 ppm) without any scaling. Similar excellent agreement is found for a test set of natural products.

They finish up with a discussion of [18]annulene 1. The structure of 1 is controversial. X-ray crystallography indicates a near D_6h geometry, but the computed NMR shifts using a D_6h geometry are in dramatic disagreement with the experimental values, leading Schleyer to suggest a C₂  geometry. Kwan and Liu applied their dynamic NMR method to the D_6h, D_3h, and C₂ structures, and find the best agreement with the experimental chemical shifts are from the dynamic NMR initiated from the D_6h geometry. Dynamic effects thus make up for the gross error found with the static geometry, and now bring the experimental and computational data into accord.

One final note on this paper. The authors indicate that they have filed a provisional patent on their method. I am disturbed by this concept of patenting a computational methodology, especially in light of the fact that many other methods have been made available to the world without any legal restriction. For example, full details including scripts to apply Tantillo’s correction method are available through the Cheshire site and a web app to implement Goodman’s DP4 method are available for free. Provisional patents are not available for review from the US Patent Office so I cannot assess just what is being protected here. However, I believe that this action poses a real concern over the free and ready exchange of computational methodologies and ideas.

 

References

(1) Kwan, E. E.; Liu, R. Y. "Enhancing NMR Prediction for Organic Compounds Using Molecular Dynamics," J. Chem. Theor. Comput. 2015, 11, 5083-5089, DOI: 10.1021/acs.jctc.5b00856.

InChIs

1: InChI=1S/C18H18/c1-2-4-6-8-10-12-14-16-18-17-15-13-11-9-7-5-3-1/h1-18H/b2-1-,3-1+,4-2+,5-3+,6-4+,7-5-,8-6-,9-7+,10-8+,11-9+,12-10+,13-11-,14-12-,15-13+,16-14+,17-15+,18-16+,18-17-
InChIKey=STQWAGYDANTDNA-DWSNDWDZSA-N

[Editors note: this paper has also been highlighted by Jan Jensen]


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Attraction or Repulsion? London Dispersion Forces Control Azobenzene Switches

Schweighauser, L.; Strauss, M. A.; Bellotto, S.; Wegner, H. A. Angew. Chem. Int. Ed. 2015, 54, 13436-13439
Contributed by Steven Bachrach
Reposted from Computational Organic Chemistry with permission

The role of dispersion in organic chemistry has been slowly recognized as being quite critical in a variety of systems. I have blogged on this subject many times, discussing new methods for properly treating dispersion within quantum computations along with a variety of molecular systems where dispersion plays a critical role. Schreiner¹ has recently published a very nice review of molecular systems where dispersion is a key component towards understanding structure and/or properties.

In a similar vein, Wegner and coworkers have examined the Z to E transition of azobenzene systems (1a-g→ 2a-g) using both experiment and computation.² They excited the azobenzenes to the Z conformation and then monitored the rate for conversion to the E conformation. In addition they optimized the geometries of the two conformers and the transition state for their interconversion at both B3LYP/6-311G(d,p) and B3LYP-D3/6-311G(d,p). The optimized structure of the t-butyl-substituted system is shown in Figure 1.

a: R=H; b: R=tBu; c: R=Me; d: R=iPr; e: R=Cyclohexyl; f: R=Adamantyl; g: R=Ph

1b

1b-TS-2b

2b

Figure 1. B3LYP-D3/6-311G(d,p) optimized geometries of 1a, 2a, and the TS connecting them.

The experiment finds that the largest activation barriers are for the adamantly  1f  and  t-butyl 1b azobenzenes, while the lowest barriers are for the parent 1a and methylated 1c azobenzenes.

The trends in these barriers are not reproduced at B3LYP but are reproduced at B3LYP-D3. This suggests that dispersion is playing a role. In the Z conformations, the two phenyl groups are close together, and if appropriately substituted with bulky substituents, contrary to what might be traditionally thought, the steric bulk does not destabilize the Z form but actually serves to increase the dispersion stabilization between these groups. This leads to a higher barrier for conversion from the Z conformer to the Econformer with increasing steric bulk.

 

References

(1) Wagner, J. P.; Schreiner, P. R. "London Dispersion in Molecular Chemistry—Reconsidering Steric Effects,"Angew. Chem. Int. Ed. 2015, 54, 12274-12296, DOI: 10.1002/anie.201503476.

(2) Schweighauser, L.; Strauss, M. A.; Bellotto, S.; Wegner, H. A. "Attraction or Repulsion? London Dispersion Forces Control Azobenzene Switches," Angew. Chem. Int. Ed. 2015, 54, 13436-13439, DOI:10.1002/anie.201506126.

 

InChIs

1b: InChI=1S/C28H42N2/c1-25(2,3)19-13-20(26(4,5)6)16-23(15-19)29-30-24-17-21(27(7,8)9)14-22(18-24)28(10,11)12/h13-18H,1-12H3/b30-29-
InChIKey=SOCNVTNVHBWFKC-FLWNBWAVSA-N

2b: InChI=1S/C28H42N2/c1-25(2,3)19-13-20(26(4,5)6)16-23(15-19)29-30-24-17-21(27(7,8)9)14-22(18-24)28(10,11)12/h13-18H,1-12H3/b30-29+
InChIKey=SOCNVTNVHBWFKC-QVIHXGFCSA-N

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Popular Highlights of 2015

Computational Chemistry Highlights received 31,663 pageviews in 2014.

A total of 63 highlights were published in 2015 and the five most viewed highlights are

1. Big Data Meets Quantum Chemistry Approximations: The ∆-Machine Learning Approach highlighted by Jan Jensen in April, 2015

2. A computational drug design success story highlighted by Jan Jensen in January, 2015

3. Accurately Modeling Nanosecond Protein Dynamics Requires at least Microseconds of Simulation highlighted by Jan Jensen in June, 2015

4. Selected publications of Stefan Grimme, Leibniz prize winner 2015 highlighted by Martin Korth in March, 2015

Tied for 5th place
5. Approaches to dispersion in DFT highlighted by David Bowler in April, 2014

5. Discovering chemistry with an ab initio nanoreactor highlighted by Alán Aspuru-Guzik in December, 2014

The most popular entries within the last 30 days can as always be found on the right hand side of this page.

The are many ways to stay updated on the latest CCH highlights and CCH currently has 218 subscribers on Feedly, 307 twitter followers, 515 Google+ followers, 179 Facebook followers, and 165 followers on Linkedin.


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