Frits
Daeyaert
a and
Michael W.
Deem
*ab
aDepartments of Bioengineering, Rice University, Houston, TX 77005, USA. E-mail: mwdeem@rice.edu
bDepartments of Physics & Astronomy, Rice University, Houston, TX 77005, USA
First published on 2nd April 2019
Zeolite beta is a crystalline material with layer-type faulting. The two end members with perfect crystalline order are beta A and beta B. While zeolite beta in faulted form is a widely used industrial catalyst, additional applications may be possible with the perfect crystalline forms. We here computationally design chemically synthesizable organic structure directing agents that may aid the nucleation and growth of pure zeolite beta A, excluding the competing product zeolite beta B.
Of these 239 known zeolites, 17 are of industrial interest.4 One of these is zeolite beta, which finds application as a catalyst for benzene alkylation and separation of aromatic compounds from aqueous phases.5,6 As with many zeolites,7 zeolite beta is synthesized by an hydro-thermal process in the presence of tetra-ethyl ammonium as structure directing agent.8 The structure of zeolite beta thus obtained is a closely inter-grown mixture of 2 polymorphs, polymorph A (BEA) and polymorph B (BEB). Of these, BEA consists of an enantiomorphic pair.9,10 While syntheses of BEA-enriched zeolite beta have been reported,11–15 the synthesis of pure BEA has until now remained elusive. More uniformly structured zeolites have the potential to be cleaner and catalytically more efficient.16 Synthesis of pure BEA would be a breakthrough in catalytic applications of zeolite beta. Synthesis of the pure BEA polymorph would also be a first step towards the enantiomerically pure or enriched substance, which would open possibilities for chiral separation and catalysis.
The use of organic structure directing agents (OSDAs) in zeolite synthesis is well established.17 Moreover, it has been shown that the structure-directing ability of an OSDA is governed by its non-bonded interaction energy with the zeolite pores.18 In previous work we have used this principle to successfully design novel OSDAs for a number of zeolites.19–22 In the present study, we build upon this experience to design OSDAs for pure BEA. We seek OSDAs that stabilize BEA but not BEB. To design selective, synthesizable OSDAs for zeolite BEA we used de novo design, virtual screening, exhaustive virtual combinatorial screening, and stochastic virtual combinatorial screening. The scoring function evaluates the stabilization energy of a putative OSDA in both the BEA and BEB forms of zeolite beta. Pareto optimization is used to design molecules that bind strongly to BEA but bind weakly to BEB.
score | score type | threshold |
---|---|---|
Force field compatibility | Binary | |
Number of rotatable bonds | ≤ | 6 |
Longest sp3–sp3 chain | ≤ | 3 |
Non-C, –N or –H atoms | ≤ | 0 |
Triply bonded C | ≤ | 0 |
C to charged N ratio | ≤ | 18 |
Chiral centers | ≤ | 0 |
Molecular volume | ≤ | 800 Å3 |
Fit in BEA | Binary | |
MD stabilization energy in BEA | Minimize | |
Energy gap MD stabilization energy in BEB | Maximize |
If the molecular volume filter was passed, an estimate for the global minimum energy conformation of the molecule was determined using a genetic algorithm24 for conformational search (Gacs). Gacs operates on a set of conformations encoded by chromosomes with the decimal encoded values of the torsion angles of the rotatable bonds in the molecule. Initially, a population of conformations with randomly chosen torsion angles between 0° and 360° is generated. The default population size is 20 × N, where N is the number of rotatable bonds. The fitness of each conformation is the molecular mechanics energy obtained by initializing the torsion angles of the molecule with the values coded by the chromosome and performing a local gradient optimization of the molecule. The force field used for the molecular mechanics minimization is the Merck molecular force field (MMFF).25 After the local optimization, the torsion angle values in the molecule are replaced by the torsion angles in the local optimal conformation. After the population is initiated, mutation and selection occur. Child conformations are generated from parent conformations by recombination and random mutation. The parent conformations are selected by tournament selection: two different conformations are selected randomly, and the one with the highest fitness is chosen as the parent. At each fitness evaluation, the torsion angles are optimized. The new conformation replaces the worst scoring conformation in the population if it has a higher fitness. If the fitness of the new conformation is worse than the worst conformation in the population, or if it is already present in the population, it is discarded. The algorithm finishes after a fixed number of fitness evaluations, by default 50 × N. The search for the global potential energy minimum of flexible molecules is a challenging problem, and only deterministic search methods can offer some guarantee that this minimum will be found. These methods, such as the interval analysis algorithm in ref. 26, are time consuming and limited to relatively small molecules. They are therefore not suitable for high-throughput applications. As Gacs is a stochastic algorithm, we cannot guarantee that the lowest energy conformation found is the global potential energy minimum. However, it has been our experience that for molecules with up to 10 rotatable bonds the same lowest energy conformer is reproducibly generated in repeated runs of the algorithm. We therefore assume that this is the global potential energy minimum. The CPU time consumed by a Gacs run is typically between 1 and 10 minutes, depending on the number of flexible bonds and the number of atoms in the molecule.
In the next step of the scoring function, a number of copies of the lowest energy conformation of the molecule obtained by the Gacs program was fitted into the unit cell of the zeolite using an optimized grid procedure.27 The number of OSDA copies fitted into the zeolite is fixed and depends on the zeolite species. It must be determined by geometric evaluation before subsequent screening and searching for promising molecules. The optimal translation of the molecule was determined by fast Fourier transform from the optimal convolution shift. The optimal rotation was obtained by repeating this procedure for 100 random orientations of the molecule. The optimal number of copies for both BEA and BEB has been determined to be eight for small ‘monomer’ molecules, and four for ‘dimer’ molecules.
When the desired number of copies of the putative OSDA had been fitted into the zeolite without large steric clashes, the stabilization energy of the OSDA in the zeolite was calculated using a molecular dynamics (MD) procedure as in ref. 27. The stabilization energy was obtained from the non-bonded Lennard-Jones interaction of the OSDA with the zeolite and the other OSDA copies in the unit cell. It is defined as E = Esystem − Ezeolite − nEOSDA where the energies are calculated as averages from molecular dynamics runs. Esystem is the energy of the zeolite with n copies of OSDAs in the unit cell, Ezeolite is the energy of the zeolite, and EOSDA is the energy of a single OSDA. After fitting the OSDA copies into the zeolite, four rounds of energy minimization were carried out. The minimized structures were used as starting points for three MD runs of 0.1, 1 and 30 ps respectively, at a temperature of 70 °C. Average energies were obtained from the last 5 ps of the production run of the third MD run. While the initial positioning of the OSDA copies uses a single, rigid conformer, the subsequent multiple rounds of MD simulation with various time steps allow the ODSA to adjust this initial conformation to the shape of the zeolite. The stabilization energy was obtained in units of kilojoule per mol Si (kJ per (mol Si)), allowing comparison of different OSDAs in the zeolite. The MD calculations were carried out with the GULP program28 using the Dreiding force field.
In a first MD calculation, the stabilization energy of the molecule in the BEA polymorph was calculated. If this stabilization energy was below the threshold of −15 kJ per (mol Si), the stabilization energy in the BEB energy was calculated, and the energy gap between the two energies was obtained. Due to the stochastic nature of the scoring protocol, there may exist computational errors in the calculation of the stabilization energies. Therefore, when molecules with a stabilization energy gap between BEA and BEB greater than 2 kJ per (mol Si) were generated in the various design runs, we a posteriori recalculated the stabilization energy in BEB of these molecules in six independent runs. We then took the lowest values of the BEB stabilization energies and used these to recalculate the gaps.
We seek to design OSDAs that bind favorably to BEA and less favorably to BEB. We used the above scoring function to design molecules that have a low binding energy to BEA and a large positive energy gap with respect to BEB. We have adopted 4 strategies in our design effort: de novo design, virtual screening of commercially available compounds, exhaustive virtual combinatorial chemistry, and stochastic virtual combinatorial chemistry.
(1) Add a reaction step to a parent synthesis route.
(2) Delete a reaction step from a parent synthesis route.
(3) Replace a reagent in a parent synthesis route by a randomly chosen different reagent.
(4) Replace a reagent in a parent synthesis route by a similar reagent.
(5) Combine two parent synthesis routes.
(6) Generate a new synthesis route from scratch.
The parent synthesis routes needed by the genetic operators were chosen by tournament selection. As child molecules were individually generated, if their fitness was better than the worst molecule in the population, they were inserted in the population by replacing the worst molecule. This generation process allowed an efficient parallelization of the GA, because no synchronization was needed in contrast to a traditional generational replacement GA. Asynchronous operation was especially important with the step-wise scoring function used in this study, as the molecules that did not pass the threshold values of the property vector were evaluated in a very short time. Conversely, molecules that required MD evaluation of their stabilization energies in both BEA and BEB required a large amount of CPU time. Parallelization was implemented using a master-worker paradigm. The master program was responsible for structure generation and optimization. Several score function daemons were run as separate stand-alone programs that calculated the fitness of the molecules generated by the de novo design algorithm. Communication between the main program and the score function daemons was through disk file semaphores. Multiple copies of the score function daemons were run on different machines with communication through NFS. For molecules that passed the threshold values of the property vector, a two-dimensional fitness needed to be optimized: the stabilization energy in BEA must be minimized, and the stabilization energy in BEB must be maximized. To allow simultaneous optimization of these two, often conflicting, fitness values, the molecules of the GA were Pareto sorted, and the de novo design produced a set of molecules that are Pareto optimal with respect to the BEA stabilization energy and the stabilization energy gap with BEB. Within this Pareto optimal set, no molecule dominated another molecule: if a molecule within the Pareto optimal set had a better stabilization energy in BEA than another molecule in the Pareto optimal set, its energy gap with BEB was worse. We have shown that the application of Pareto sorting not only allows simultaneous optimization of multiple fitness criteria, but also makes the GA more efficient.30 At present, 100 organic chemistry reactions are implemented in the de novo design program. As reagent database we have used a set of 39500 commercially available chemical building blocks. With these reagents, a synthesis route comprising a single reaction step can generate 118 × 103 zero-order and 203 × 106 first-order reaction products. Assuming a constant expansion factor, the number of compounds generated in a synthesis route comprising N reaction steps can be estimated as 39
520 × [(118 × 103 + 203 × 106)/39
520]N. To limit synthetic complexity, the number of reactions in a reaction scheme was limited to three. With this limitation, the available chemical search space consists of an estimated 5.3 × 1015 compounds.
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Scheme 1 Dimerization of a monomer ODSA. ArN is an aromatic 5- or 6- membered N-heterocycle. N may or may not be bound to H, X is a halogen, L is a linker with 1 up to 6 C atoms between the halogens. |
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Scheme 2 De novo design of monomers: Syn069824. The predicted stabilization energy in BEA is −16.2 kJ per (mol Si). |
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Scheme 3 De novo design of monomers: Syn304344. The predicted stabilization energy in BEA is −17.0 kJ per (mol Si). |
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Scheme 4 De novo design of monomers: Syn074355. The predicted stabilization energy in BEA is −15.3 kJ per (mol Si). |
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Scheme 5 De novo design of monomers: Syn189538. The predicted stabilization energy in BEA is −15.6 kJ per (mol Si). |
The putative monomer OSDAs obtained by the de novo design runs were derivatized in two ways. First, compounds formed from reactants containing a pyridine functionality were replaced by their phenyl analogues, as exemplified in Scheme 6. Second, molecules with alkylatable aromatic nitrogen atoms were virtually methylated as exemplified in Scheme 7. In addition to extending the number of compounds, this latter modification ensures that upon dimerization with a dihalogen linker the resulting dimers will have a quaternary ammonium functionality that is typical of effective OSDAs. Subsequent combinations of the two virtual derivatizations led to a total of 2988 molecules that were scored. Of these, 170 compounds were predicted to have a stabilization energy in BEA equal to or below −15 kJ per (mol Si).
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Scheme 6 Replacement of a pyridine functionality by the corresponding commercially available phenyl analog. |
We also examined the tetra-hydro indazole ‘THI’ shown in Table 2. It was found to have a stabilization energy of −17.9 kJ per (mol Si). Therefore, the eMolecules building block database35 was searched for analogues of these structures through the substructure search functionality. A set of 122 of these were directly scored, and 18 were found to have a stabilization energy equal to or below −15 kJ per (mol Si) threshold. The 3 top scoring tetra-hydro indazole analogs are also shown in Table 2.
The result of the 3 design routes above is a set of 346 putative monomer OSDAs that have a stabilization energy below −15 kJ per (mol Si). Of these, 271 have an aromatic N functionality suited for dimerization with a dihalide linker.
In addition, 271 × 271 × 78 = 5728
398 asymmetric dimers can be formed consisting of a linker and two different monomer OSDAs. This number is no longer amenable to an exhaustive MD calculation. Instead, the stochastic virtual combinatorial screening protocol was used to search the asymmetric dimer molecular space. As it has been our experience that this protocol is quite effective in searching very large chemical spaces, we extended the molecular space by including monomers identified in the de novo design that pass the simple molecular filters of the scoring function in Table 1, even if they had a stabilization energy above −15 kJ per (mol Si). As there are 2996 of these, the chemical space to be searched contains 2996 × 2996 × 78 ≈ 700 × 106 molecules. We performed two runs to search this molecular space, one that was allowed to evaluate a total of 20
000 molecules, and one that was allowed to evaluate a total of 100
000 molecules. The first run produced 166 dimers with a stabilization energy in BEA below −15 kJ per (mol Si), the second run produced 564 dimers with a stabilization energy in BEA below −15 kJ per (mol Si). The molecules forming the Pareto front are shown Tables 4 and 5.
run | MD runs | BEA ≤ −15 kJ | BEA ≤ −15 kJ and gap ≥ 2 kJ | BEA ≤ −15 kJ and gap ≥ 2 kJ per 1000 MD runs | Pareto |
---|---|---|---|---|---|
Exhaustive dimers | 11![]() |
18 | 5 | 0.44 | 3 |
Stochastic dimers 1 | 5493 | 169 | 17 | 3.09 | 5 |
Stochastic dimers 2 | 18![]() |
571 | 95 | 5.01 | 4 |
de novo 1 molecules | 5731 | 405 | 38 | 6.63 | 7 |
de novo 2 molecules | 8122 | 436 | 57 | 7.02 | 9 |
Both algorithms are multi-objective genetic algorithms that seek to generate a front of Pareto-optimal molecules, i.e. molecules that have both a low stabilization energy in BEA, and a large energy gap with respect to BEB. This is illustrated in Fig. 1. The color-coded dots in this figure represent all molecules with a stabilization energy below or equal to −15 kJ per (mol Si) found by the 5 design runs, and the solid lines represent the Pareto fronts for each run.
Table 8 also lists the numbers of compounds with a stabilization energy equal to or below −15 kJ per (mol Si) in BEA found in each run. Except for 23 compounds that were found in the two stochastic dimers runs, no overlap between these sets of compounds was found. This indicates that in each run, different parts of the chemical space were searched. A total of 1579 unique molecules were found that stabilize BEA with a stabilization energy equal to or below −15 kJ per (mol Si) BEA. How these cover the chemical space is illustrated in Fig. 2, which shows the first and second principal coordinates of the molecules as obtained from a Tanimoto similarity matrix. The compounds generated by the two stochastic dimers runs occupy the same region of the chemical space, which can be ascribed to the smaller search space of the stochastic algorithm, and which explains the overlap of 23 molecules between the search results. The two de novo design runs occupy relatively different regions of the chemical space.
In the 5 design runs, the molecule with the lowest stabilization energy for BEA with an energy gap with respect to BEB larger than 2 kJ per (mol Si) is the third molecule listed in Table 6, with identifier Syn148049, which was generated in the first de novo design run. The stabilization energy in BEA is −16.4 kJ per (mol Si), and the energy gap with respect to BEB is 40.2 kJ per (mol Si). Fig. 3 shows the Van der Waals surface renderings of the unit cell of Syn148049 inside BEA and BEB. This figure shows in a qualitative way how the shape of the designed OSDA is highly complementary to the shape of BEA. In contrast, the channels of the BEB zeolite are not fully occupied by the guest molecule. Fig. 4 shows the position of the 4 distinct copies of Syn148049 in BEA in atomic detail.
In efforts to synthesize BEA enriched zeolite beta, a number of ODSAs have been investigated.11,14,15,34,36 From these references, we selected those OSDAs reported to be effective in BEA formation and calculated their stabilization energies. These were obtained by fitting 4, 6, and 8 copies of the OSDAs in BEA and performing the MD simulation. The lowest stabilization energies obtained for the OSDAs as well as the corresponding number of copies in BEA are listed in Table 9. The lowest stabilization energy is −14.1 kJ per (mol Si) for compound B82, with 6 OSDA copies in BEA. The lowest stabilization energy for a compound with 4 OSDA copies in BEA is −13.3 kJ per (mol Si) for compound E96. Both compounds are shown in Fig. 5. It may be appreciated that the stabilization energies of the compounds designed in this work are significantly lower than the stabilization energies of the existing OSDAs.
Compound | Reference | Stabilization energy (kJ per (mol Si)) | Copies in BEA |
---|---|---|---|
B82 | 34 | −14.1 | 6 |
iPenMP | 36 | −13.6 | 6 |
iProMP | 36 | −13.5 | 8 |
B71 | 34 | −13.4 | 6 |
E96 | 34 | −13.3 | 4 |
EDMCHOH | 11 | −13.3 | 6 |
iButMP | 36 | −13.2 | 6 |
E95 | 34 | −13.1 | 4 |
B204 | 34 | −13.1 | 4 |
A07 | 34 | −12.9 | 6 |
B75 | 34 | −12.7 | 6 |
TMCHOH | 11 | −12.7 | 6 |
B108 | 34 | −12.6 | 4 |
A61 | 34 | −12.6 | 6 |
B172 | 34 | −12.5 | 6 |
E32 | 34 | −12.1 | 4 |
B203 | 34 | −12.0 | 6 |
E39 | 34 | −11.6 | 4 |
B27 | 34 | −11.6 | 6 |
B130 | 34 | −11.6 | 6 |
B08 | 34 | −11.6 | 4 |
DMDPOH | 11 | −11.4 | 8 |
A69 | 34 | −11.4 | 4 |
B81 | 34 | −11.3 | 4 |
A60 | 34 | −11.2 | 6 |
E51 | 34 | −11.0 | 4 |
B125 | 34 | −10.8 | 4 |
A70 | 34 | −10.7 | 4 |
TEA | 14 and 15 | −10.7 | 6 |
G101 | 34 | −10.0 | 4 |
DMPOH | 11 | −10.0 | 6 |
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Fig. 5 Best scoring OSDAs from ref. 11, 14, 15, 34 and 36, their stabilization energy in BEA, and the corresponding number of copies in BEA. |
In the studies described in ref. 34, 36, both BEA forming and non-BEA forming OSDAs are reported. We computed that the BEA-forming OSDAs have an average stabilization energy of −12.1 ± 1.0 kJ per (mol Si). The average stabilization energy of the non-BEA forming OSDAS is −10.8 ± 1.7 kJ per (mol Si). While the formation of BEA does not solely depend on the OSDA used but also on the specific reaction parameters and the stabilization energy in other zeolite structures, the observation that the experimentally BEA forming OSDAs have lower calculated stabilization energies lends support to our scoring protocol.
In the present study, we have used all-silica models of the zeolites BEA and BEB. The use of zeolites as catalysts depends on the presence of charge centers that act as Lewis acids and that are provided by replacement of Si atoms by metals such as Al and Cu. As more detailed studies on the reaction mechanisms become available from quantum mechanical studies, e.g. (ref. 37), it will become interesting to influence and steer the siting of these metallic sites with the aid of computational design strategies such as detailed in the present study. This would require, to begin with, the inclusion of a Coulomb energy term in the calculation of the OSDA-zeolite stabilization energies in addition to the currently used Van der Waals potential. We will address this problem in future research.
While zeolite beta consists of a close intergrowth of the BEA and BEB polymorphs, in our design model we consider the interaction of putative OSDAs with perfect BEA and BEB structures. Increase of BEA content of zeolite beta can be achieved either by an increase in the occurrence of small BEA domains, or the presence of larger BEA domains. Structural characterization of BEA-enriched zeolite beta has shown that the enrichment involves the presence of larger BEA domains in this material.11 We can therefore assume that OSDAs interacting favorably with pure BEA can effectively lead to BEA enriched zeolite beta.
Our de novo design program generates not only chemically correct molecular structures, but also virtual synthesis routes from well-established organic chemistry reactions and available building blocks. While the proposed synthesis routes may not be the most efficient ones to produce their outcome, it has been shown that on average approximately two thirds of the routes are feasible with reasonable effort.29 Our method to computationally design OSDAs has been validated in previous studies. In a first study, as a proof of principle, a novel OSDA for STW zeolite was designed, synthesized and successfully used to produce the target zeolite.21 Next, a novel OSDA was designed, synthesized and successfully used to produce zeolite SSZ-39 under highly variable reaction conditions.20 Also, an alternative, cheaper OSDA that produced zeolite SSZ-52, a zeolite that has potential application in engine exhaust clean-up, was designed.19 Finally, using the Pareto based multi-objective approach also deployed in the present study, a chiral OSDA to generate, for the first time, enantiomerically enriched STW zeolite was discovered.22 In the present study, a large but tractable number of putative OSDAs to selectively guide the synthesis of BEA were obtained using the combined methods of de novo design, virtual screening, exhaustive combinatorial chemistry and stochastic combinatorial chemistry. From these compounds, those that can be synthesized with the least effort and cost can be chosen for synthesis and zeolite formation.
Footnote |
† Electronic supplementary information (ESI) available: A .sdf file containing the 212 compounds with a stabilization energy in zeolite beta A lower than −15 kJ per (mol Si) and an energy gap greater than 2 kJ per (mol Si) with respect to zeolite beta B. See DOI: 10.1039/c8ta11913a |
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