Simulations of Chemical Reactions with the Frozen Domain Formulation of the Fragment Molecular Orbital Method

Hiroya Nakata, Dmitri G. Fedorov, Takeshi Nagata, Kazuo Kitaura, and Shinichiro Nakamura. Journal of Chemical Theory and Computation 2015, 11, 3053−3064
Contributed by +Jan Jensen

Reprinted (adapted) with permission from J. Chem. Theory Comput. 2015, 11, 3053−3064. Copyright (2015) American Chemical Society

I am highlighting this paper because it is the first paper I have come across that reports the optimized TS, free energy barrier, and IRC for an enzymatic reaction using an all-QM description of the entire enzyme.

The underlying method is the frozen domain with dimers (FDD) formulation of the fragment molecular orbital method (FMO) implemented in the GAMES program.  The FMO is fragmentation method and in the FDD formulation the system is divided into three domain: A) an active domain where the both the geometry and density are allowed to change, B) a polarizable buffer where only the density is allowed to change and F) a frozen domain where neither is allowed to change.  The latter restraints means that the fragments in the frozen domain only have to be calculated once.

This paper presents the implementation of the fully analytic gradient and Hessian at the RHF level and the interface to the IRC methodology in GAMESS.  (The interface to the TS-optimization code was reported previously using a different variant of FMO.)  In this approach only the Hessian of the active domain is computed.

The method is then applied to the keo-enol tautomerization of phosphoglycolohydroxamic acid (PGH) by triosephosphate isomerase (TIM).  The active domain is PGH and the proton donor Glu410 while the polarizable buffer is any residue or water molecule within 5.2 Å of the active domain, which were both treated at the RHF/6-31G(d) + dispersion level of theory.  The frozen domain, i.e. the rest of the TIM monomer, is treated at the RHF/STO-3G level of theory and the entire system is comprised of 9227 atoms.

The workflow was at follows using 128 2.93 GHz Xeon cores:

1. Constrained optimization to obtain TS guess (12 hrs)
2. Hessian calculation (24 hrs)
3. TS optimization (12 hrs)
4. Hessian calculation (24 hrs)
5. IRC calculations (16 points) in each direction (42 hrs)
6. Optimization of reactants and products starting from last IRC points (12 hrs each)
7. Hessian calculation for reactant and products (24 hrs each)

Of course, at this level of theory and with such a small active domain the resulting free energy barrier (21.4 kcal/mol) is considerably different from the experimental value (14 kcal/mol) but this is only a proof-of-concept study.

An important next step for FMO studies of enzyme catalysis will be the implementation of a mixed DFT/RHF-D model where all or part of the active domain can be treated with DFT.  The computational cost-increase associated with using DFT could be off-set by using, for example, HF-3c for the non-reactive part of of the active region as well as the buffer region since this method gives excellent structures as low computational cost.

I thank +Casper Steinmann for alerting me to this article


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On the tunneling instability of a hypercoordinated carbocation

Kozuch, S. Phys. Chem. Chem. Phys. 2015, 17, 16688-16691
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Last year I wrote a post on the possibility of a stable hypercoordinated carbon in the C(CH₃)₅⁺ molecule as proposed by Schleyer and Schaefer.¹ Kozuch has re-examined this molecule with an eye towards examining the lifetime of this proposed “fleeting” molecule.²

The computed barriers for either (1) loss of a methane molecule leaving behind the (CH₃)₂C⁺CH₂CH₃cation or (2) loss of an ethane molecule leaving behind the t-butyl cation are small: 1.65 and 1.37 kcal mol^-1, respectively. Kozuch employed canonical variational theory with and without small curvature tunneling (SCT). Without the tunneling correction, the pentamethylmethyl cation is predicted to have a long (millennia) lifetime at very low temperatures (<20 K). However, when tunneling is included, the half-life is reduced to 6 and 40 μs for degradation along the two pathways. Clearly, this is not a fleeting molecule – its lifetime is really too short to consider it as anything.

Interestingly, perdeuterating the molecule ((CD₃)₅C⁺) substantially increases the half-life to 4 ms, a thousand-fold increase. Tritium substitution would further increase the half-life to 0.2 s – a long enough time to really identify it and perhaps justify the name “molecule”. What is perhaps the most interesting aspect here is that H/D substitution has such a large effect on the tunneling rate even though no C-H bond is broken in the TS! This results from a mass effect (a CH₃ vs. a CD₃ group is migrating) along with a zero-point vibrational energy effect.

References

(1) McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. "Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?," Angew. Chem. Int. Ed. 2014, 53, 7875-7878, DOI: 10.1002/anie.201403314.

(2) Kozuch, S. "On the tunneling instability of a hypercoordinated carbocation," Phys. Chem. Chem. Phys.2015, 17, 16688-16691, DOI: 10.1039/C5CP02080H.

InChIs

C(CH₃)₅⁺: InChI=1S/C6H15/c1-6(2,3,4)5/h1-5H3/q+1
InChIKey=GGCBGJZCTGZYFV-UHFFFAOYSA-N

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Inverted Carbon Geometries: Challenges to Experiment and Theory

Bremer, M.; Untenecker, H.; Gunchenko, P. A.; Fokin, A. A.; Schreiner, P. R. J. Org. Chem. 2015, 80, 6520–6524
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Inverted carbon atoms, where the bonds from a single carbon atom are made to four other atoms which all on one side of a plane, remain a subject of fascination for organic chemists. We simply like to put carbon into unusual environments! Bremer, Fokin, and Schreiner have examined a selection of molecules possessing inverted carbon atoms and highlights some problems both with experiments and computations.¹

The prototype of the inverted carbon is propellane 1. The ­C_inv-C_inv bond distance is 1.594 Å as determined in a gas-phase electron diffraction experiment.² A selection of bond distance computed with various methods is shown in Figure 1. Note that CASPT2/6-31G(d), CCSD(t)/cc-pVTZ and MP2 does a very fine job in predicting the structure. However, a selection of DFT methods predict a distance that is too short, and these methods include functionals that include dispersion corrections or have been designed to account for medium-range electron correlation.

CASPT2/6-31G(d) CCSD(T)/cc-pVTZ MP2/cc-pVTZ MP2/cc-pVQZ B3LYP/6-311+G(d,p) B3LYP-D3BJ/6-311+G(d,p) M06-2x/6-311+G(d,p)	1.596 1.595 1.596 1.590 1.575 1.575 1.550

Figure 1. Optimized Structure of 1 at MP2/cc-pVTZ, along with C_inv-C_inv distances (Å) computed with different methods.

Propellanes without an inverted carbon, like 2, are properly described by these DFT methods; the C-C distance predicted by the DFT methods is close to that predicted by the post-HF methods.

The propellane 3 has been referred to many times for its seemingly very long C_inv-C_inv bond: an x-ray study from 1973 indicates it is 1.643 Å.³ However, this distance is computed at MP2/cc-pVTZ to be considerably shorter: 1.571 Å (Figure 2). Bremer, Fokin, and Schreiner resynthesized 3 and conducted a new x-ray study, and find that the C_inv-C_inv distance is 1.5838 Å, in reasonable agreement with the computation. This is yet another example of where computation has pointed towards experimental errors in chemical structure.

Figure 2. MP2/cc-pVTZ optimized structure of 3.

However, DFT methods fail to properly predict the C_inv-C_inv distance in 3. The functionals B3LYP, B3LYP-D3BJ and M06-2x (with the cc-pVTZ basis set) predict a distance of 1.560, 1.555, and 1.545 Å, respectively. Bremer, Folkin and Schreiner did not consider the ωB97X-D functional, so I optimized the structure of 3 at ωB97X-D/cc-pVTZ and the distance is 1.546 Å.

Inverted carbon atoms appear to be a significant challenge for DFT methods.

References

(1) Bremer, M.; Untenecker, H.; Gunchenko, P. A.; Fokin, A. A.; Schreiner, P. R. "Inverted Carbon Geometries: Challenges to Experiment and Theory," J. Org. Chem. 2015, 80, 6520–6524, DOI:10.1021/acs.joc.5b00845.

(2) Hedberg, L.; Hedberg, K. "The molecular structure of gaseous [1.1.1]propellane: an electron-diffraction investigation," J. Am. Chem. Soc. 1985, 107, 7257-7260, DOI: 10.1021/ja00311a004.

(3) Gibbons, C. S.; Trotter, J. "Crystal Structure of 1-Cyanotetracyclo[3.3.1.1^3,7.0^3,7]decane," Can. J. Chem.1973, 51, 87-91, DOI: 10.1139/v73-012.

InChIs

1: InChI=1S/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYSA-N

3: InChI=1S/C11H13N/c12-7-9-1-8-2-10(4-9)6-11(10,3-8)5-9/h8H,1-6H2
InChIKey=KTXBGPGYWQAZAS-UHFFFAOYSA-N

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Computational and Experimental Investigations of the Formal Dyotropic Rearrangements of Himbert Arene/Allene Cycloadducts

Pham, H. V.; Karns, A. S.; Vanderwal, C. D.; Houk, K. N.  J. Am. Chem. Soc. 2015,137, 6956-6964
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Houk and Vanderwal have examined the dyotropic rearrangement of an interesting class of polycyclic compounds using experimental and computational techniques.¹ The parent reaction takes the bicyclo[2.2.2]octadiene 1 into the bicyclo[3.2.1]octadiene 3. The M06-2X/6-311+G(d,p)/B3LYP/6-31G(d) (with CPCM simulating xylene) geometries and relative energies are shown in Figure 1. The calculations indicate a stepwise mechanism, with an intervening zwitterion intermediate. The second step is rate determining.

1 (0.0)	TS1 (35.6)
2 (21.9)	TS2 (40.1)
3 (-4.2)

Figure 1. B3LYP/6-31G(d) and relative energies (kcal mol^-1) at M06-2X/6-311+G(d,p).

Next they computed the activation barrier for the second TS for a series of substituted analogs of 1, with various electron withdrawing group as R₁ and electron donating groups as R₂, and compared them with the experimental rates.

Further analysis was done by relating the charge distribution in these TSs with the relative rates, and they find a nice linear relationship between the charge and ln(k_rel). This led to the prediction that a cyano substituent would significantly activate the reaction, which was then confirmed by experiment. Another prediction of a rate enhancement with Lewis acids was also confirmed by experiment.

A last set of computations addressed the question of whether a ketone or lactone would also undergo this dyotropic rearrangement. The lactam turns out to have the lowest activation barrier by far.

References

(1) Pham, H. V.; Karns, A. S.; Vanderwal, C. D.; Houk, K. N. "Computational and Experimental Investigations of the Formal Dyotropic Rearrangements of Himbert Arene/Allene Cycloadducts," J. Am. Chem. Soc. 2015,137, 6956-6964, DOI: 10.1021/jacs.5b03718.

InChIs

1: InChI=1S/C11H11NO/c1-12-10(13)7-9-6-8-2-4-11(9,12)5-3-8/h2-5,7-8H,6H2,1H3
InChIKey=MNYYUIQDOAXLTK-UHFFFAOYSA-N

2: InChI=1S/C11H13NO/c1-12-10(13)6-9-3-2-8-4-5-11(9,12)7-8/h4-6,8H,2-3,7H2,1H3
InChIKey=YFHRGVKBIORUIF-UHFFFAOYSA-N

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.