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. 2025 Nov 14;129(47):11003–11013. doi: 10.1021/acs.jpca.5c05284

A Comparison of Electronic Structure Methods for Predicting the Hydrogenation Energies of Candidate Molecules for Hydrogen Storage

Amanda Dumi †, Shiv Upadhyay †, Hassan Harb ‡, Rajeev S Assary ‡, Dan C Sorescu §,∥, Kenneth D Jordan †,∥, Anouar Benali ⊥,*
PMCID: PMC12670397  PMID: 41234149

Abstract

The development of novel energy materials and fuels is required to expand current available energy sources. Aiming to reach this goal, there is growing interest in using molecular hydrogen as an energy carrier due to its abundance and high energy density. Liquid organic hydrogen carriers (LOHCs) are a promising route to the large-scale storage and transport of hydrogen for use in the energy economy. The search for thermodynamically viable LOHC molecules for real world use has led to a set of constraints on the dehydrogenation enthalpy and the minimum gravimetric hydrogen capacity. These constraints allow one to formulate the search for an ideal LOHC candidate molecule as an optimization problem well suited to the strengths of machine learning and artificial intelligence computational approaches. A critical barrier to a large-scale, high-throughput screening of LOHC candidate molecules is the lack of reliable training data. Computational electronic structure methods including density functional theory, coupled cluster approximations, and diffusion Monte Carlo can be used to provide training data where experimental data are either unreliable or do not exist. In this work, we use these methods to calculate the dehydrogenation energies and enthalpies of candidate LOHC molecules.

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Introduction

The development of novel energy materials and fuels is required to meet the need to move toward affordable and reliable energy sources. To drive affordable and resilient energy fuels, interest in molecular hydrogen as an energy carrier has been growing due to its abundance and high energy density. , The concept of using molecular hydrogen as an energy carrier has been around for decades, and the term “hydrogen economy” was coined in 1972 by Bockris and Appleby to refer to the network of producing, transporting, and using hydrogen on a large scale. , However, large-scale storage and transport of molecular hydrogen remains challenging. An alternative approach of chemically storing hydrogen in unsaturated liquid hydrocarbon molecules called LOHCs has gained recent interest. ,− LOHCs are unsaturated organic compounds that can chemically bind and release molecular hydrogen in a catalyst-mediated cycle of hydrogenation and dehydrogenation, under specific reaction conditions. ,,, By being implemented in a recyclable manner, LOHCs can contribute to a resilient and affordable energy system. − LOHCs, with their high hydrogen storage capacity and energy density, are suitable for portable applications and offer a better safety profile than hydrogen gas, making them ideal for transportation and safety-critical uses. ,−

The selection of an ideal LOHC requires careful consideration of several critical properties. , Primary among these is the dehydrogenation enthalpy, which should ideally fall within the range of 9.6–16.7 kcal/mol H2. , This range, based on multiple experimental studies of previously reported LOHCs, ensures that the hydrogen-rich LOHC can retain hydrogen over extended periods, yet not so tightly that it cannot be readily released when needed. Another major consideration is the requirement of a minimum gravimetric hydrogen capacity of 5.5% wt H2, a condition set forth by the U.S. Department of Energy (DOE) to ensure a basic level of energy efficiency in potential LOHCs. Beyond these energy-related parameters, the kinetics of the LOHCs must also be efficient, with the ability to undergo multiple hydrogenation and dehydrogenation cycles facilitated by a suitable catalyst. ,,− Finally, the selection process also accounts for several other key factors including the material’s commercial availability, toxicity, stability, flammability, and its ability to exist in a liquid state at room temperature. − All these considerations, while individually important, collectively dictate the suitability and performance of a molecule as a LOHC.

Prominent LOHC dehydrogenated/hydrogenated pairs, such as benzene/cyclohexane, , toluene/methyl cyclohexane, and N-ethylcarbazole/perhydro-N-ethylcarbazole , have been extensively investigated for large-scale hydrogen storage and transportation due to their favorable attributes such as low dehydrogenation enthalpies (within the desired range of 9.6–16.7 kcal/mol H2) and high hydrogen storage capacities, exceeding the DOE’s 5.5% threshold. ,, However, these systems are accompanied by several limitations: for instance, benzene is carcinogenic N-ethylcarbazole is a solid at room temperature with a melting point of 68 °C, posing practical application challenges, , and toluene and methyl cyclohexane, are classified as highly flammable due to their low flash points of −3 and 6 °C, respectively. Further compounding these limitations are the catalytic cycles for hydrogenation and dehydrogenation, which often occur under high temperature and pressure conditions mediated by precious metal catalysts. This limits their effectiveness, safety, and practicality. Additionally, several LOHC systems are prone to side reactions and degradation processes and experience less than complete hydrogenation, which results in a hydrogen storage capacity below theoretical expectations, thereby diminishing their reusability and overall efficiency. These challenges highlight the need for the discovery of new, efficient, and sustainable LOHCs.

The computational exploration of the vast chemical space of unsaturated organic molecules presents a formidable challenge, making it a prime candidate for machine learning (ML) techniques to facilitate the rapid evaluation of numerous potential molecules. − Many studies rely on density functional theory (DFT) to generate training data ML models. While DFT methods have been used to characterize LOHCs in previous studies , and for reaction energies in general, there is no guarantee DFT will be adequate for unexplored forms of LOHCs. In fact, in previous studies it was shown that commonly employed DFT approaches can exhibit errors of several kcal/mol in hydrogenation enthalpies, which hinders the identification and appraisal of viable LOHC molecules. − To enhance the discovery of LOHCs, accurate quantum chemical methods that consistently predict hydrogenation energies correctly to within 1 kcal/mol per molecule of H2 are imperative.

In cases where DFT falls short, many-body methods such as diffusion Monte Carlo (DMC) − and low-scaling coupled cluster methods emerge as powerful tools that can achieve a balance of accuracy and computational feasibility. The applicability of DMC to ML efforts has been demonstrated by Tenti et al. and Huang et al. Additionally, DMC has been successfully used to describe hydrogen reactions on surfaces. − Low-scaling coupled cluster methods have been used in assessing conformer energies, and creating reference databases for organic molecules.

In this work, we explore the performance of ab initio methods including DMC and domain based local pair-natural orbital coupled cluster singles, doubles, and perturbative triples (DLPNO-CCSD­(T)) to predict the hydrogenation energies and enthalpies of a series of molecules that are of interest as LOHCs but for which the ωB97X-D, B3LYP, − and MO6–2X DFT functionals have proven inadequate. Since the performance of these density functional approximations varies, we also calculated the hydrogenation energies and enthalpies of this set of molecules with the ωB97M-V functional. This functional was selected because of its exhaustive parametrization process and its recent successes on similar bond-breaking processes. −

Theoretical Methods

Molecule Selection and Generation

To construct a data set suitable for benchmarking, we sourced molecules that were utilized as a starting set for LOHC discovery in a previous study. The primary rationale behind the selection of these molecules was their known experimental dehydrogenation enthalpies, an essential parameter for understanding their efficacy as LOHCs. Additionally, the majority of the molecules in this set have been previously identified as potential candidates for LOHC systems. In cultivating the data set, the Simplified Molecular Input Line Entry System (SMILES) strings , reported in Table S1 of the Supporting Information were converted to 3D structures using the RDKIT package and were optimized using the universal force field (UFF) method. For systems where multiple conformers were possible further refinement was done by first optimizing the geometries of the various conformers using the Frequency, Geometry Noncovalent, eXtended tightbinding (GFNN-xTB) DFT method together with the conformer–rotamer ensemble sampling tool (CREST) driver. In cases that the UFF and CREST calculations gave two or more low-energy conformers, these structures were reoptimized at the ωB97X-D/6-31G­(2df,p) − level of theory, and the lowest energy conformer from these calculations was used for the subsequent calculations unless noted otherwise. For a subset of the molecules DLPNO-CCSD­(T) calculations were also carried out using the ωB97M-V geometries, with results summarized in the Supporting Information. These calculations gave hydrogenation energies very close to those obtained using the B3LYP optimized geometries.

We recognize potential uncertainties in reported experimental dehydrogenation values due to various factors. Contemporary calorimeters are subject to errors arising from calibration uncertainties, thermal leakages, or baseline drifts; deviations during calibration, for instance, that can distort enthalpy measurements. − Challenges also persist in fully saturating LOHCs with hydrogen, as highlighted by studies showing dibenzyl toluene’s hydrogen loading reaching only about 90% of its theoretical capacity. Furthermore, LOHCs are susceptible to side reactions, especially at high hydrogenation/dehydrogenation temperatures. Molecules such as N-ethyl carbazole can undergo ancillary reactions due to suboptimal conditions, catalyst inefficiencies, or the tendency of N-alkyl substituents in carbazoles to dissociate prematurely. This, along with the presence of multiple conformers and unaccounted low-lying isomers with varying thermodynamics, can skew the actual enthalpy measurements. Finally, variability in experimental parameters such as temperature and pressure can further introduce discrepancies in the reported data.

Density Functional Theory Calculations

Starting from the geometries in the previous section, the geometries of all species considered were reoptimized all-electron using both the B3LYP − and ωB97M-V density functional methods, together with the cc-pVQZ basis set , obtained from the Basis Set Exchange. − These calculations were performed using the PySCF software version 2.1.0. ,− The coupled cluster and DMC calculations used the B3LYP-optimized geometries. For a subset of the molecules domain based lower pair-natural orbital (DLPNO)-coupled cluster singles, doubles, and perturbative triples (CCSD­(T)) calculations were also carried out using the ωB97M-V geometries, with results summarized in the Supporting Information. These calculations gave hydrogenation energies very close to those obtained using the B3LYP optimized geometries.

In addition, harmonic vibrational frequencies were calculated at the ωB97M-V/aug-cc-pVTZ , level of theory using geometries optimized with this basis set and functional. These calculations were performed using the ORCA version 5.0 software. The harmonic frequencies were used to obtain the estimates of the vibrational zero-point energies (ZPEs) and thermal corrections to facilitate comparison with experiment. The rigid rotor approximation was also used in obtaining the thermal corrections. A summary of these corrections can be found in Table S5. Unscaled vibrational frequencies were used for ZPE and thermal corrections. The scaling of the computed vibrational frequencies to approximately account for anharmonic effects was found to have a minimal impact on the computed hydrogenation energies, and this analysis is included in the Supporting Information.

Coupled-Cluster Methods

For all species considered, hydrogenation energies were calculated using the DLPNO-CCSD­(T) method, treating all electrons and employing the frozen-core approximation and the cc-pVQZ basis set. CCSD­(T) calculations with the local natural orbital (LNO) and DLPNO approximations were found to give similar energetics. , A summary of this comparison can be found in Table S2. In addition, the energetics of the C6H6 + 3H2 → C6H12 reaction was calculated using the LNO-coupled cluster singles, doubles, and triples (CCSDT) method, in which the triples term is treated nonperturbatively. Due to the computational demands of the LNO-CCSD­(T) and LNO-CCSDT calculations they were carried out with the smaller cc-pVDZ basis. , Finally, a PNO-space extrapolation was conducted to assess the impact of the PNO-space truncation. , The extrapolation had little impact on the hydrogenation energy for most systems (∼0.01 kcal/mol mean change over the test set) and was unstable for four of the systems studied here. Therefore, we chose to use DLPNO calculations at a single (TightPNO) threshold. All coupled cluster calculations were performed using ORCA version 5.0 with the LNO-CCSDT calculations utilizing the MRCC software interface. ,

Quantum Monte Carlo Methods

DMC is a real-space stochastic approach to solving the many-body Schrödinger equation. The method is particularly attractive given its low scaling with the number of electrons and the highly parallelizable algorithms. Being a real space method, DMC energies are much less sensitive to the choice of the atomic basis set than methods working in a space of Slater determinants.

When dealing with fermionic particles, the DMC method requires the use of the fixed-node approximation to maintain the antisymmetric property of the wave function. For efficient sampling and to reduce statistical fluctuations, Slater-Jastrow trial wave functions are used. The nodes of the trial wave function are set through one or more Slater determinants comprised of single-particle orbitals, which in this work are expanded in a B-spline basis. Single determinant (SD) trial wave functions for DMC calculations made use of B3LYP orbitals, while the multideterminant (MD) trial wave functions were generated by the configuration interaction using a perturbative selection (CIPSI) procedure with iteratively refined natural orbitals.

To reduce the cost of the DMC calculations as well as to reduce the fluctuations near the ionic core regions, the core-correlated electron core potential (ccECP) pseudopotentials were used for all elements. The pseudopotentials replaced the 1s electrons for period two elements (e.g., C, O, N), but no electrons were replaced for H. These pseudopotentials were designed to be used with high-accuracy many-body methods such as DMC. To address errors introduced by the use of nonlocal pseudopotentials a modified version of the T-moves algorithm, denoted as ‘v3′ in the QMCPACK user’s manual, was used.

The SD DMC calculations were carried out using trial wave functions expanded in both the ccECP-cc-pVTZ and ccECP-cc-pVQZ basis sets. The dehydrogenation energies obtained from these two sets of calculations are nearly identical, so for the SD-DMC calculations only the results with the ccECP-cc-pVQZ basis set are reported here. Also, considering this close agreement, only the smaller ccECP-cc-pVTZ basis set was used for the multideterminant DMC calculations.

As noted above, the trial wave functions for the DMC calculations also include Jastrow factors that are symmetric with electron exchange and reduce the variance. The Jastrow factors contain terms for one-body (electron–ion), two-body (electron–electron) and three-body (electron–electron–ion) interactions. In this study, 10 parameters were employed per spin-channel for the one- and two-body Jastrow factors and 26 parameters for the three-body Jastrow factor. Since many molecules were considered in this work, the Jastrow cutoff distances were not optimized for each system. Instead default distances were fixed to 10 Bohr for the one- and two-body terms and 5 Bohr for the three-body term for all systems. The parameters in the Jastrow function were optimized by minimizing the energy using the linear method in variational Monte Carlo (VMC). The DMC calculations were done using a time step of 0.001 Ha–1. The quantum Monte Carlo (QMC) calculations were done in QMCPACK version 3.17. ,

Selected Configuration Interaction Calculations

To reduce the fixed-node errors in DMC energies, one can employ trial wave functions comprised of multi-Slater determinants rather than just one. Here we use CIPSI, which is a selected configuration interaction (SCI) method, to identify a compact determinant expansion, while not requiring the full Hilbert space. In this work, the quality of the nodal surface is explored by comparing DMC energies for a single Slater determinant trial wave function to those employing multi-Slater determinant expansions of various sizes as generated by CIPSI. The initial CIPSI calculations were performed with a single Slater determinant wave function of Hartree–Fock (HF) orbitals and employing ccECP pseudopotentials and the corresponding ccECP-cc-pVTZ basis set. The multideterminant expansions were created by first generating small expansions and forming natural orbitals to use in generating larger expansions. Various trial wave functions are constructed by truncating the large expansion according to the magnitude of the configuration interaction (CI) coefficients. For generating the truncated trial wave functions the following values were used to screen the magnitude of the CI coefficient: 1 × 10–2, 1 × 10–3, 1 × 10–4. The CIPSI calculations were done using Quantum Package 2.

Definition of the Hydrogenation Energy

The hydrogenation energies per H2 molecule are calculated as

ΔEhyd=Eh−(Edh+NH2×EH2)NH2 1

where E h (E dh) is the total energy of the hydrogenated (dehydrogenated) species, N H2 denotes the moles of H2, and E H2 is the energy of a single H2 molecule. These energies were corrected for vibrational ZPE and thermal corrections calculated at T = 298.15 K and compared with experimental values of the enthalpies of dehydrogenation (Table S1). To enhance the discovery of LOHCs, accurate quantum chemical methods that consistently predict hydrogenation energies correctly to within 1 kcal/mol per molecule of H2 are imperative.

Results and Discussion

In the following sections, we compare the performance of DLPNO-CCSD­(T) against less approximate coupled cluster methods. We then use DLPNO-CCSD­(T) as the reference for the hydrogenation energies to explore the performance of the B3LYP and ωB97M-V DFT methods and of SD-DMC. For selected systems, we examine the impact of orbital optimization of the SD trial wave functions on the DMC energies. We examine improvements in the DMC hydrogenation energies upon adoption of MD trial wave functions. Finally, the ZPE and thermally corrected results are compared with experiment.

Performance of DLPNO-CC Methods for Hydrogenation Energy Prediction

For the subset of molecules for which we carried out both LNO-CCSD­(T) and DLPNO-CCSD­(T) calculations, we find that the two methods give hydrogenation energies that agree to within 0.3 kcal/mol per H2 molecule (see Figure S1 and Table S2 in the Supporting Information). In addition, for the benzene + 3H2 → cyclohexane reaction we find that the DLPNO-CCSD­(T)/cc-pVDZ hydrogenation energy is close to that from the LNO-CCSDT/cc-pVDZ calculations in which the triples are treated nonperturbatively (agreeing to within 0.2 kcal/mol per H2). We also established that the DLPNO-CCSD­(T) values of the hydrogenation energies calculated with the cc-pVQZ basis set are close to those obtained with the cc-pVTZ basis set, leading us to conclude that the DLPNO-CCSD­(T) hydrogenation energies are well converged with the cc-pVQZ basis set. When corrected for vibrational ZPE and thermal effects, the computed value of the benzene hydrogenation energy per H2 molecule is within 0.5 kcal/mol of the experimental value, which will be further discussed in a following section. These results lead us to conclude that the DLPNO-CCSD­(T)/cc-pVQZ calculations are appropriate for providing benchmark numbers for assessing the performance of the other theoretical approaches considered.

Assessing the Performance of DMC and DFT Methods for ΔE hyd

In this section, the performance of SD-DMC, B3LYP, and ωB97M-V DFT methods to predict hydrogenation energies is explored. Figure reports the differences between the hydrogenation energies from the DFT and SD-DMC calculations and the results of the DLPNO–CCSD­(T) calculations. The performance of each method in terms of their Mean Absolute Error (MAE)­s for the entire data set are summarized in Table . The dehydrogenation energies from the SD-DMC calculations have a MAE of 1.7 kcal/mol per H2 molecule compared to the DLPNO–CCSD­(T) results. For comparison, we note that the corresponding MAEs for the B3LYP and ωB97M-V functionals are 2.53 and 0.26 kcal/mol, respectively.

1.

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Signed error with respect to the DLPNO-CCSD­(T) reference of ΔE hyd values from SD-DMC (green circles) and the B3LYP (black circles) and ωB97M-V (purple circles) calculations. The “(trans)” label indicates that the trans isomer of the hydrogenated species was used.

1. Summary of the MAE in the ΔE hyd Values from ωB97M-V, B3LYP, and SD-DMC as Compared with DLPNO-CCSD­(T) for the 30 Systems in the Test Set .

method MAE kcal/mol
ωB97M-V 0.26
B3LYP 2.53
SD-DMC 1.70
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a

These results are without ZPE or thermal corrections.

Multideterminant Trial Wave Functions for DMC

As noted above, the SD-DMC hydrogenation energies differ on average by about 1.70 kcal/mol per H2 from the DLPNO-CCSD­(T) values. Moreover, in all cases, the SD-DMC calculations give more negative hydrogenation energies than the DLPNO-CCSD­(T) calculations. The major source of this discrepancy is expected to be fixed node errors in the SD-DMC calculations which are expected to be higher in the unsaturated than in the saturated compounds.

Figure reports for benzene and cyclohexane the CIPSI variational energy with the second-order perturbative correction, E var. + E PT2, as a function of the number of Slater determinants in the variational space as well as the DMC energy as a function of the number of Slater determinants in the trial wave function. As expected, the CIPSI E var. + E PT2 energies converge slowly with increasing number of determinants. However, as the number of determinants is increased from one to about 1000, the CIPSI E var. + E PT2 energy drops more rapidly for benzene than for cyclohexane. While the DMC energies show more rapid convergence, they are still not well converged when employing 2 × 106 Slater determinants in the trial wave functions. Moreover, while the DMC energy of cyclohexane is nearly constant as the trial wave function grows from 1 to ∼6 × 104 determinants and then undergoes an appreciable energy lowering upon further expansion to ∼106 determinants, the DMC energy of benzene steadily decreases as the number of Slater determinants is increased, with an appreciable energy lowering in going from 1 to 500 determinants in the trial wave function. These results illustrate the challenge in balancing the nodal surface error when comparing two different chemical species.

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Change in the CIPSI and DMC energies of benzene and cyclohexane as a function of the number of Slater determinants. The energies are reported relative to the single determinant HF energy.

One approach to balance wave function quality for two systems is variance matching. Figure reports the variance per electron for the CIPSI variational energies of benzene and cyclohexane as a function of the number of Slater determinants generated using the CIPSI method. As seen in the figure, the variance per electron of benzene with a threshold giving ∼100 SDs for the trial wave function is approximately equal to that of cyclohexane with only one Slater determinant.

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Variance per electron of the CIPSI energies as a function of the number of Slater determinants for benzene and cyclohexane.

Additionally, we explored the variance per electron in the DMC energies of benzene and cyclohexane as a number of Slater determinants in the trial wave functions with the results being reported in Figure . We note that the variance of H2 is negligible and is not included. It is seen from this figure that for benzene one needs to employ ∼1000 Slater determinants in the MD-DMC calculations to achieve the same variance per electron as obtained for the SD-DMC calculations on cyclohexane.

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Variance per electron (Ha2) in the DMC energies of benzene and cyclohexane as a function of the number of Slater determinants in the trial wave functions.

The results of the calculations on benzene and cyclohexane suggest the following strategy for reducing the fixed-node bias in the DMC energies: namely employing SD trial wave functions for the hydrogenated species and multideterminant trial wave functions with a truncation of 0.001 on the coefficient of the multideterminant expansion for the dehydrogenated species. To test this strategy, six additional systems were treated with the results being shown in Figure . The figure also reports the corresponding results for benzene and cyclohexane. As seen from this figure, the errors in the DMC values of the hydrogenation energies of six of the seven systems considered are significantly reduced when employing a truncation of 0.001 on the CI coefficients for the unsaturated species. Moreover, for four of the systems, there is a small reduction in the error when employing a truncation of 0.01.

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Differences (kcal/mol) between DMC and DLPNO-CCSD­(T) values of ΔE hyd as a function of the number of determinants in the trial wave functions for the subset of seven systems.

Optimizing the Orbitals of the Trial Wave Functions for DMC

We next turn to orbital optimization as a way to improve the nodal surface of the SD trial wave function. For this test we use benzene and pyrazine together with their hydrogenated products. In generating the orbital optimized trial wave functions, the coefficients of the occupied orbitals were optimized together with the parameters in the Jastrow factors using the VMC procedure and allowing rotations among the 200 lowest lying (occupied and unoccupied) orbitals. The resulting trial wave functions were then employed in SD-DMC calculations on benzene pyrazine and their hydrogenated products. As seen from the results reported in Table the errors in the hydrogenation energies from SD-DMC calculations are not reduced within statistical errors when using the trial wave functions with the VMC-optimized orbitals.

2. Differences in the Values of ΔE hyd (kcal/mol H2) from SD-DMC, with and without Orbital Optimization, from the DLPNO-CCSD­(T) Results.
  benzene pyrazine
SD-DMC 1.64 ± 0.53 2.40 ± 0.53
orbital optimized SD-DMC 1.76 ± 0.25 2.42 ± 0.24
MD-DMC 0.81 ± 0.62 1.96 ± 0.68
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Comparison with Experiment

In this section the calculated values of ΔH hyd are compared with available experimental values listed in Table S1. For this comparison, the calculated reaction energies were corrected for ZPE, thermal, and enthalpic contributions. Figure reports the deviations of the ΔH hyd values from the ωB97M-V, SD-DMC, and DLPNO-CCSD­(T) calculations from experiment. A summary of the MAE of each of these methods, as well as B3LYP, over the entire test set is presented in Table . For both ωB97M-V and DLPNO-CCSD­(T) the MAEs of the calculated ΔH hyd values with respect to experiment are less than 0.9 kcal/mol. The corresponding MAEs for B3LYP and SD-DMC calculations are 2.8 and 1.5 kcal/mol, respectively. For most of the systems considered the SD-DMC calculations underestimate the heat of reaction per H2 molecule by ∼2 kcal/mol, consistent with the errors caused by the fixed node bias discussed earlier in the manuscript. For 4-aminopyridine the SD-DMC, DLPNO-CCSD­(T) and the ωB97M-V all give a value of the heat of reaction considerably larger than the experimental value, suggesting an error in the experimental result in this case.

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Differences between the calculated (DFT with the ωB97M-V functional, SD-DMC, and DLPNO-CCSDT) and experimental values of ΔH hyd per mol H2. The “(trans)” label indicates that the trans isomer of the hydrogenated species was used.

3. MAEs in the Calculated Heats of Reaction per mol H2 Relative to the Experimental Values .

method MAE kcal/mol
ωB97M-V 0.82
B3LYP 2.85
SD-DMC 1.56
DLPNO-CCSD(T) 0.75
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a

The calculated results include corrections for vibrational ZPE and thermal corrections.

Conclusions

In this work, the performance of various electronic structure methods for describing hydrogenation energies of LOHCs was explored. Specifically, the methods considered were DLPNO-CCSD­(T), DFT with the ωB97M-V and B3LYP functionals, and DMC using single determinant, multideterminant, and orbital optimized trial wave functions. We find that both DLPNO-CCSD­(T) and the ωB97M-V density functional methods give ΔE hyd values in good agreement with experimental data, with MAEs less than 0.9 kcal/mol H2.

Single determinant DMC calculations result in a MAEs of 1.6 kcal/mol compared to the experiment. It is shown that using small multideterminant trial functions for the unsaturated molecules can reduce the MAE in the DMC ΔE hyd values to under 1 kcal/mol H2. In contrast, optimizing the orbitals for the trial wave function in VMC did not make a significant impact on the resulting SD-DMC values of the hydrogenation energies.

Although DFT calculations with the ωB97M-V functional give hydrogenation energies in good agreement with the results of DLPNO-CCSD­(T) and with multideterminant DMC, it is not clear that it will perform as well for other LOHC candidates as it has for those examined here. For systems that resemble the candidate molecules included in this data set, DFT calculations employing the ωB97M-V functional are expected to provide a low-cost approach for screening LOHC candidates. For more challenging systems, DLPNO-CCSD­(T) or multideterminant DMC calculations may be required.

Supplementary Material

jp5c05284_si_001.pdf (323.8KB, pdf)

Acknowledgments

A.D. and S.U. thank Dr. Eric Berquist for useful discussions regarding the ωB97M-V functional and its implementation in different codes. This research was supported in part by the University of Pittsburgh Center for Research Computing and Data, RRID:SCR_022735, through the resources provided. Specifically, this work used the H2P cluster, which is supported by NSF award number OAC-2117681. This research has used resources (Polaris machine) of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. H.H. and R.S.A. acknowledge the support by Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. H.H. and R.S.A. also acknowledge the computing resources provided on “BEBOP” and “Improv”, two computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory (ANL). AD (DLPNO-CCSD(T), DFT, and QMC calculations) and AB (sCI and QMC calculations) were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences Program and Center for Predictive Simulation of Functional Materials. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC (NTESS), a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration (DOE/NNSA) under contract DE-NA0003525. This written work is authored by an employee of NTESS. The employee, not NTESS, owns the right, title and interest in and to the written work and is responsible for its contents. Any subjective views or opinions that might be expressed in the written work do not necessarily represent the views of the U.S. Government. The publisher acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this written work or allow others to do so, for U.S. Government purposes. The DOE will provide public access to results of federally sponsored research in accordance with the DOE Public Access Plan.

The data that support the findings of this study are openly available in the Materials Data Facility , at 10.18126/p2h4-yb73.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.5c05284.

  • Summary of the experimental enthalpies of hydrogenation, comparison between localized coupled cluster methods, analysis of the CIPSI selected configuration interaction results, and complete set of computed hydrogenation energies (PDF)

#.

High Energy Density Physics Theory, Sandia National Laboratories, Albuquerque, NM 87185, United States

∇.

Department of Chemistry, University of Washington, Seattle, WA 98195, United States.

○.

Qubit Pharmaceuticals Inc., Boston, MA 02116, United States.

The authors declare no competing financial interest.

Published as part of The Journal of Physical Chemistry A special issue “J. Karl Johnson Festschrift”.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

jp5c05284_si_001.pdf (323.8KB, pdf)

Data Availability Statement

The data that support the findings of this study are openly available in the Materials Data Facility , at 10.18126/p2h4-yb73.

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