Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks

Lin Shen, Jingheng Wu, and Weitao Yang (2016)
Contributed by Jan Jensen

There has been a lot of work on estimating high level energies from low level energies, most of which have focussed some kind of interpolation or extrapolation.  However, this has been particularly challenging for QM/MM-MD studies where thousands of semiempirical energies contribute to the PMF but only hundreds of high level calculations are feasible. 

Yang and co-workers offer an interesting solution to this problem by using the high level calculations to train a neutral network to estimate the energy correction, which can then be used to estimate the high level energies for all thousands of geometries from the semiempirical QM/MM-MD.  Thus, the PMF can be computed "from scratch" at the high level rather than correcting the low level PMF.

The approach is based on work by Behler and Parrinello, but with three tweaks geared towards this particular problem.

1. The neural network is trained to reproduce an energy correction rather than a total energy.

2. Mulliken charges are used as input, in addition to atomic coordinates of the QM region, to provide some information about the interaction with the MM environment.

3. A subnet is added to the neutral net that depends on the reaction coordinate and the potential of mean force obtained at the low level to improve accuracy.  

The method is tested for three relatively small systems in water, so that high level PMFs can be computed rigorously for comparison. The results are quite impressive. For example, the free energy of glycine zwiterion is ca 8 kcal/mol higher in energy than the neutral form at the SCC-DFT/MM level but ca 8 kcal/mol lower in free energy at the B3LYP/6-31G(d)//MM level of theory. This latter value is reproduced to within 0.1 kcal/mol by the machine learning approach using only 500 B3LYP/6-31G(d)//MM energies to train the neural net. For comparison, the PMF requires 50,000 energy evaluations.

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Polytriangulane

Allen, W. D.; Quanz, H.; Schreiner, P. R. J. Chem. Theory Comput. 2016, 12, 4707–4716

Contributed by Steven Bachrach
Reposted from Computational Organic Chemistry with permission

Cyclopropyl rings can be joined together in a spiro fashion to form triangulanes. An interesting topology can be made by joining the rings to form a helical pattern, as shown in the [9]triangulane 1 below. Allen, Quanz, and Schreiner¹ have examined the notion of an infinite helical molecule formed in this way.

1

First, they describe how one can generate the coordinates of such a beast using a closed analytical expression, which is a really nice demonstration of applied geometry. Next, they compute the geometry of a series of [n]triangulanes at M06-2x/6-31G(d). The geometries of [9]triangulane and their largest example, [42]triangulane 2 are shown in Figure 1.

1

2

Figure 1. M06-2x/6-31G(d) optimized geometries of 1 and 2.

They show that the geometry of 2 exhibits a structure that has two different C-C distances: one between the spiro carbons, and the second between the spiro carbon and the methylene carbon. The distance between the spiro carbons is rather short (1.458 Å), suggesting that the bonding here is between carbons that are nearly sp²-hybridized.

Lastly, they discuss the thermodynamics of polytriangulane. They employ a series of homodesmotic reactions to attempt to determine the enthalpy for adding another cyclopropyl ring to an extended triangulane. Unfortunately, the computed enthalpy is quite dependent on functional used. Similar attempts to define the strain energy is also flawed in this way. However, regardless of the functional the enthalpy for adding a cyclopropane ring appears to reach an asymptote rather quickly. So, using [3]triangulane they estimate that the strain energy per mole of cyclopropane in triangulane is about 42.7 kcal mol^-1, or about 14 kcal mol^-1 of strain due to the spiroannulation.

References

(1) Allen, W. D.; Quanz, H.; Schreiner, P. R. “Polytriangulane,” J. Chem. Theory Comput. 2016, 12, 4707–4716, DOI: 10.1021/acs.jctc.6b00669.

InChIs

1: InChI=1S/C19H22/c1-2-12(1)5-14(12)7-16(14)9-18(16)11-19(18)10-17(19)8-15(17)6-13(15)3-4-13/h1-11H2/t14-,15-,16-,17-,18-,19-/m0/s1
InChIKey=XBTZCZDSKVTALB-DYKIIFRCSA-N

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Enediyne Cyclization on Au(111)

de Oteyza, D. G.; Paz, A. P.; Chen, Y.-C.; Pedramrazi, Z.; Riss, A.; Wickenburg, S.; Tsai, H.-Z.; Fischer, F. R.; Crommei, M. F.; Rubio, A. J. Amer. Chem. Soc. 2016, 138, 10963–10967
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

The Bergman cyclization and some competitive reactions are discussed in detail in Chapter 4 of by book. The Bergman cyclization makes the C₁-C₆ bond from an enediyne. Another, but rarer, option is to make the C₁-C₅ bond, the Schreiner-Pascal cyclization pathway. de Oteyza and coworkers have examined the competition between these two pathways for 1 on a gold surface, and used STM and computations to identify the reaction pathway.¹

The two pathways are shown below. The STM images identify 1 as the reactant on the gold surface and the product is 6. No other product is observed.

Projector augmented wave (PAW) pseudo-potential computations using the PBE functional were performed for the reaction on a Au (111) surface was modeled by a 7 x 7 x 3 supercell. The optimized geometries of the critical points are show in Figure 1.

1
TS(1→2)	TS(1→3)
2	3
TS(2→6)	TS(3→5)
6	5

Figure 1. Optimized geometries of the critical points on the two reaction pathways.

Explicit values of the relative energies are not given in either the paper or the supporting information, but rather a plot shows the relative positions of the critical points. The important points are the following: (a) the barrier for the C₁-C₅ cyclization is lower than the barrier for the C₁-C₆ cyclization and 3 is lower in energy than 2; (b) 5 is lower in energy than 6; and (c) the barrier for taking 2 to 6 is significantly below the barrier taking 3 into 5. The barrier for the phenyl migration taking 3 into 5 is so high because of a strong interaction between the carbon radical and a gold atom of the surface. The authors suggest that the two initial cyclizations are reversible, but the very high barrier for forming 5 precludes it from taking place, leaving only the route to 6 as a viable pathway.

References

(1) de Oteyza, D. G.; Paz, A. P.; Chen, Y.-C.; Pedramrazi, Z.; Riss, A.; Wickenburg, S.; Tsai, H.-Z.; Fischer, F. R.; Crommei, M. F.; Rubio, A. “Enediyne Cyclization on Au(111),” J. Amer. Chem. Soc. 2016, 138, 10963–10967, DOI: 10.1021/jacs.6b05203.

InChIs

1: InChI=1S/C22H14/c1-3-9-19(10-4-1)15-17-21-13-7-8-14-22(21)18-16-20-11-5-2-6-12-20/h1-14H
InChIKey=XOJSMLDMLXWRMT-UHFFFAOYSA-N

2: InChI=1S/C22H14/c1-3-9-17(10-4-1)21-15-19-13-7-8-14-20(19)16-22(21)18-11-5-2-6-12-18/h1-14H
InChIKey=DAUFPUDTOKPCMX-UHFFFAOYSA-N

3: InChI=1S/C22H14/c1-3-9-17(10-4-1)15-22-20-14-8-7-13-19(20)16-21(22)18-11-5-2-6-12-18/h1-14H
InChiKey=>FYBPBPGPMCJQNF-UHFFFAOYSA-N

4: InChI=1S/C22H14/c1-3-9-17(10-4-1)20-15-19-13-7-8-14-21(19)22(16-20)18-11-5-2-6-12-18/h1-14H
InChIKey=CYXVOOSYXXUHFV-UHFFFAOYSA-N

5: InChI=1S/C22H14/c1-3-9-17(10-4-1)15-19-16-22(18-11-5-2-6-12-18)21-14-8-7-13-20(19)21/h1-14H
InChIKey=BIKDAEZYYCKGSI-UHFFFAOYSA-N

6: InChI=1S/C22H14/c1-3-9-15(10-4-1)19-17-13-7-8-14-18(17)21-20(22(19)21)16-11-5-2-6-12-16/h1-14H
InChIKey=GAXPSSOZJDJRPN-UHFFFAOYSA-N

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Redox-Dependent Transformation of a Hydrazinobuckybowl between Curved and Planar Geometries

Higashibayashi, S.; Pandit, P.; Haruki, R.; Adachi, S.-I.; Kumai, R. Angew. Chem. Int. Ed. 2016, 55, 10830-10834
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Higashibayashi and co-workers prepared the hydrazine-substituted Buckyball fragment 1a and also its mono- and deoxidized analogues.¹ To interpret their results, they also computed the parent structure 1bat ωB97Xd/6-311+G(d,p).

1a R = tBut 1b R = H

The optimized structure of 1b is a bowl, but a twisted geometry, where the lone pair on each
nitrogen is on the opposite face of the molecule, lies only 1.6 kcal mol^-1 higher in energy. The barrier for moving from the bowl to the twist form is 2.0 kcal mol^-1. The completely planar structure, which is also a transition state for inversion of the bowl, lies 5.1 kcal mol^-1 above the lowest energy bowl structure. The geometries and energies of the conformations are shown in Figure 1.

1b bowl (0.0)	1b twist (1.6)
1b TS (2.0)	1b planar TS (5.11)

Figure 1. ωB97Xd/6-311+G(d,p) optimized
geometry and relative energy (kcal mol^-1) of the conformations of 1b.

The mono oxidized 1b^.+ structure is also a bowl, but there is no twist form and inversion takes place through a planar structure that is only 0.5 kcal mol^-1 above the bowl ground state. The structures and energies of these conformations of 1b^.+ are shown in Figure 2.

1b.+ bowl (0.0)

1b.+ planar TS (0.5)

Figure 2. ωB97Xd/6-311+G(d,p) optimized geometry and relative energy (kcal mol^-1) of the conformations of 1b^.+.

Lastly, the di-oxidized 1b²⁺ is planar, and its structure is shown in Figure 3.

1b2+ planar

Figure 2. ωB97Xd/6-311+G(d,p) optimized geometry of 1b²⁺.

These computations corroborate all of the experimental data observed with 1a. What is particularly of note is the fact that the potential energy surface is so dependent on charge state: a three-well potential for the neutral, and two-well potential for the monocation, and a single-well potential for the dication.

References

(1) Higashibayashi, S.; Pandit, P.; Haruki, R.; Adachi, S.-I.; Kumai, R. “Redox-Dependent
Transformation of a Hydrazinobuckybowl between Curved and Planar Geometries,” Angew. Chem. Int. Ed.2016, 55, 10830-10834, DOI: 10.1002/anie.201605340.

InChIs

1a: InChI=1S/C40H44N2/c1-37(2,3)21-13-25-26-14-22(38(4,5)6)19-31-32-20-24(40(10,11)12)16-28-27-15-23(39(7,8)9)18-30-29(17-21)33(25)41(34(26)31)42(35(27)30)36(28)32/h13-20H,1-12H3
InChIKey=DKJNIDLSMMQIBX-UHFFFAOYSA-N

1b:InChI=1S/C24H12N2/c1-5-13-14-6-2-11-19-20-12-4-8-16-15-7-3-10-18-17(9-1)21(13)25(22(14)19)26(23(15)18)24(16)20/h1-12H
InChIKey=JQNPHLTXAOKXNQ-UHFFFAOYSA-N

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Dynamically Complex [6+4] and [4+2] Cycloadditions in the Biosynthesis of Spinosyn A

Patel, A; Chen, Z. Yang, Z; Gutierrez, O.; Liu, H.-W.; Houk, K. N.; Singleton, D. A.  J. Amer. Chem. Soc. 2016,138, 3631-3634
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Enzyme SpnF is implicated in catalyzing the putative [4+2] cycloaddition taking 1 into 3. Houk, Singleton and co-workers have now examined the mechanism of this transformation in aqueous solution but without the enzyme.¹ As might be expected, this mechanism is not straightforward.

Reactant 1, transition states, and products 2 and 3 were optimized at SMD(H2O)/M06-2X/def2-TZVPP//B3LYP-D3(BJ)//6-31+G(d,p). Geometries and relative energies are shown in Figure 1. The reaction1 → 2 is a formal [6+4] cycloaddition, and the reaction 1 → 3 is a formal [4+2] cycloaddition. Interestingly, only a single transition state could be located TS1. It is a bispericyclic TS (see Chapter 4 of my book), where these two pericyclic reaction sort of merge together. After TS1 is traversed the potential energy surface bifurcates, leading to 2 or 3. This is yet again an example of a single TS leading to two different products. (See the many posts I have written on this topic.) The barrier height is 27.6 kcal mol^-1, with 2 lying 13.1 kcal mol^-1 above 3. However, the steepest descent pathway from TS1 leads to 2. There is a second transition state TScope that describes a Cope rearrangement between 2 and 3. Using the more traditional TS theory description, 1 undergoes a [6+4] cycloaddition to form 2 which then crosses a lower barrier (TScope) to form the thermodynamically favored 3, which is the product observed in the enzymatically catalyzed reaction.

1 (0.0)
TS1 (27.6)
2 (4.0)	3 (-9.1)
(24.7)

Figure 1. B3LYP-D3(BJ)//6-31+G(d,p) optimized geometries and relative energies in kcal mol^-1.

Molecular dynamics computations were performed on this system by tracking trajectories starting in the neighborhood of TS1 on a B3LYP-D2/6-31G(d) PES. The results are that 63% of the trajectories end at 2, 25% end at 3, and 12% recross back to reactant 1, suggesting an initial formation ratio for 2:3 of 2.5:1. The reactions are very slow to cross through the “transition zone”, typically 2-3 times longer than for a usual Diels-Alder reaction (see this post).

Once again, we see an example of dynamic effects dictating a reaction mechanism. The authors pose a tantalizing question: Can an enzyme control the outcome of an ambimodal reaction by altering the energy surface such that the steepest downhill path from the transition state leads to the “desired” product(s)? The answer to this question awaits further study.

References

(1) Patel, A; Chen, Z. Yang, Z; Gutierrez, O.; Liu, H.-W.; Houk, K. N.; Singleton, D. A. “Dynamically
Complex [6+4] and [4+2] Cycloadditions in the Biosynthesis of Spinosyn A,” J. Amer. Chem. Soc. 2016,138, 3631-3634, DOI: 10.1021/jacs.6b00017.

InChIs

1: InChI=1S/C24H34O5/c1-3-21-15-12-17-23(27)19(2)22(26)16-10-7-9-14-20(25)13-8-5-4-6-11-18-24(28)29-21/h4-11,16,18-21,23,25,27H,3,12-15,17H2,1-2H3/b6-4+,8-5+,9-7+,16-10+,18-11+/t19-,20+,21-,23-/m0/s1
InChIKey=JEKALMRMHDPSQK-ZTRRSECRSA-N

2: InChI=1S/C24H34O5/c1-3-19-8-6-10-22(26)15(2)23(27)20-12-11-17-14-18(25)13-16(17)7-4-5-9-21(20)24(28)29-19/h4-5,7,9,11-12,15-22,25-26H,3,6,8,10,13-14H2,1-2H3/b7-4-,9-5+,12-11+/t15-,16-,17-,18-,19+,20+,21-,22+/m1/s1
InChIKey=AVLPWIGYFVTVTB-PTACFXJJSA-N

3: InChI=1S/C24H34O5/c1-3-19-5-4-6-22(26)15(2)23(27)11-10-20-16(9-12-24(28)29-19)7-8-17-13-18(25)14-21(17)20/h7-12,15-22,25-26H,3-6,13-14H2,1-2H3/b11-10+,12-9+/t15-,16+,17-,18-,19+,20-,21-,22+/m1/s1
InChIKey=BINMOURRBYQUKD-MBPIVLONSA-N

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