Binding Energies Of Clusters Research Articles

Molecular dynamic simulations of displacement cascades in Molybdenum and Molybdenum-Rhenium alloys

Molybdenum-Rhenium (Mo-Re) alloys are considered core materials for advanced nuclear reactor components due to their excellent mechanical properties, machinability, and resistance to irradiation damage. However, irradiation-induced embrittlement and phase precipitation at high temperatures, along with transmutation nuclides, have hindered their broader application. To address this, we developed a Mo-Re interatomic potential using the Finnis-Sinclair formalism, facilitating molecular dynamics simulations to study primary irradiation damage. Systemically primary irradiation damage simulations for Mo and Mo-Re alloys have been performed. It’s found that there were more Frenkel-pair defects produced during the stage of thermal spike in Mo-Re alloys but fewer defects survived at the end of the cascade compared to Mo. In addition, the number of large-size interstitial clusters and dislocation loops was higher in Mo-Re alloys than in pure Mo with the same PKA energy. This is mainly attributed to the fact that Mo-Re alloys have lower thermal conductivity, while the binding energies of interstitial clusters and dislocation loops with sizes less than 100 in Mo-Re alloys are comparable to those of pure Mo, resulting in higher defect composites and larger defect sizes in Mo-Re alloys. These findings provide valuable insights into the primary damage mechanisms in Mo-Re alloys under irradiation, offering a foundation for developing kinetic models to simulate radiation-induced microstructural evolution.

Energetics of vacancy clusters in TiVTaW low-activation high-entropy alloy investigated by ab initio calculations

High-entropy alloys (HEAs) have attracted attention as potential candidates for nuclear fusion reactor materials due to their superior mechanical properties and irradiation resistance. The TiVTaW low-activation HEA exhibits an especially large variation in the cohesive energies of the pure metals of its alloying elements, leading to the characteristic of energetically heterogeneous atomic environments that differ at each atomic site, a focal point of this study. To evaluate the influence of this site-to-site variation on vacancy cluster formation, in this study, density functional theory calculations were conducted on small vacancy clusters consisting of the nearest neighbor configurations in equimolar TiVTaW. The monovacancy formation energies in TiVTaW were found to span a significantly broader range compared to those in other HEAs. Moreover, the range of vacancy cluster formation energies in TiVTaW was observed to be nearly identical to the range of the vacancy cluster formation energies of its alloying elements in the pure metals. Our calculations also showed that clusters with five or fewer vacancies exhibit a lower mean binding energy compared to the pure metals of the alloying elements, indicating that vacancy clusters in TiVTaW are less stable than those in pure metals. Additionally, the distribution of cluster binding energies for sizes less than five-vacancy clusters was found to range from −1.60 to 3.12 eV, which includes unstable clusters with negative binding energies. These energetic characteristics arising from the heterogeneous atomic environments unique to HEAs can influence void nucleation under irradiation. Furthermore, based on a thermodynamic model, local maxima in the free energy change correlating with cluster size were observed during the nucleation of vacancy clusters, indicating the generation of metastable small vacancy clusters. These findings provide a new perspective on irradiation damage mechanisms in general HEAs.

Decomposition and Growth Pathways for Ammonium Nitrate Clusters and Nanoparticles.

Understanding the formation and decomposition mechanisms of aerosolized ammonium nitrate species will lead to improvements in modeling the thermodynamics and kinetics of aerosol haze formation. Studying the sputtered mass spectra of cation and anion ammonium nitrate clusters can provide insights as to which growth and evaporation pathways are favored in the earliest stages of nucleation and thereby guide the development and use of accurate models for intermolecular forces for these systems. Simulated annealing Monte Carlo optimization followed by density functional theory optimizations can be used reliably to predict minimum-energy structures and interaction energies for the cation and anion clusters observed in mass spectra as well as for neutral nanoparticles. A combination of translational and rotational mag-walking and sawtooth simulated annealing methods was used to find optimum structures of the various heterogeneous clusters identifiable in the mass spectra. Following these optimizations with ωB97X-D3 density functional theory calculations made it possible to rationalize the pattern of peaks in the mass spectra through computation of the binding energies of clusters involved in various growth and dissociation pathways. Testing these calculations against CCSD(T) and MP2 predictions of the structures and binding energies for small clusters demonstrates the accuracy of the chosen model chemistry. For the first time, the peaks corresponding with all detectable species in both the positive and negative ion mass spectra of ammonium nitrate are identified with their corresponding structures. Thermodynamic control of particle growth and decomposition of ions due to loss of ammonia or nitric acid molecules is indicated. Structures and interaction energies for larger (NH4NO3)n nanoparticles are also presented, including the prediction of new particle morphologies with trigonal pyramidal character.

Density Functional Theory Study of Triple Transition Metal Cluster Anchored on the C2N Monolayer for Nitrogen Reduction Reactions.

The electrochemical nitrogen reduction reaction (NRR) is an attractive pathway for producing ammonia under ambient conditions. The development of efficient catalysts for nitrogen fixation in electrochemical NRRs has become increasingly important, but it remains challenging due to the need to address the issues of activity and selectivity. Herein, using density functional theory (DFT), we explore ten kinds of triple transition metal atoms (M3 = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) anchored on the C2N monolayer (M3-C2N) as NRR electrocatalysts. The negative binding energies of M3 clusters on C2N mean that the triple transition metal clusters can be stably anchored on the N6 cavity of the C2N structure. As the first step of the NRR, the adsorption configurations of N2 show that the N2 on M3-C2N catalysts can be stably adsorbed in a side-on mode, except for Zn3-C2N. Moreover, the extended N-N bond length and electronic structure indicate that the N2 molecule has been fully activated on the M3-C2N surface. The results of limiting potential screen out the four M3-C2N catalysts (Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N) that have a superior electrochemical NRR performance, and the corresponding values are -0.61 V, -0.67 V, -0.63 V, and -0.66 V, respectively, which are smaller than those on Ru(0001). In addition, the detailed NRR mechanism studied shows that the alternating and enzymatic mechanisms of association pathways on Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N are more energetically favorable. In the end, the catalytic selectivity for NRR on M3-C2N is investigated through the performance of a hydrogen evolution reaction (HER) on them. We find that Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N catalysts possess a high catalytic activity for NRR and exhibit a strong capability of suppressing the competitive HER. Our findings provide a new strategy for designing NRR catalysts with high catalytic activity and selectivity.

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [Kanungo, B. J. Phys. Chem. Lett. 2024, 15, 323-328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN 50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree-Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

Revealing the critical role of vanadium in radiation damage of tungsten-based alloys

Refractory tungsten-based medium- and high-entropy alloys form a promising class of strong, heat- and radiation-resistant materials for nuclear applications. Here, we systematically explore the radiation tolerance of Mo–Nb–Ta–V–W alloys using molecular dynamics simulations and a machine-learned interatomic potential. Going from pure W to W-based equiatomic binaries, ternaries, quaternary, and the quinary high-entropy alloy, we simulate the radiation damage accumulation up to 0.4–0.8 dpa through cumulative collision cascades. We find that the radiation damage and evolution are controlled by a combination of cascade-induced clustering, the balance in migration of vacancies and interstitials, and defect cluster binding energies. These mechanisms are strongly influenced by atom size, among which vanadium as the smallest atom is decisive. In pure W and alloys without V, the microstructure is characterised by large and growing interstitial dislocation loops. In stark contrast, in alloys containing V, vacancy dislocation loops are formed directly in collision cascades and the balanced migration rate of vacancies and interstitials promotes recombination and prevents growth of interstitial loops. The atom size differences also lead to clear segregation, with small atoms (V) in interstitial clusters and larger atoms (Ta, Nb) segregating around vacancy clusters. Furthermore, the small cluster sizes, formation of vacancy loops, segregation, and balanced migration in V-containing alloys lead to low swelling and an exceptionally efficient defect annealing compared to pure W and V-free alloys. Our results highlight WTaV as a promising low-activation material, where almost 90% of defects are annealed at 2000 K during 5 ns compared to <20% in pure W.

Density functional theory study on the beryllium clusters doped with silicon atom

An all-electron calculation on BenSi (n = 1–12) clusters has been performed by using density functional theory with the generalized gradient approximation at the PW91 level. The results reveal that the lowest energy geometries of BenSi (n = 1–12) clusters may be generated by substituting a Si atom for one Be atom of the Ben+1 clusters. In addition, Si atom tends to occupy external locations of main Ben clusters and bonds with multiple Be atoms in the BenSi (n > 2) clusters. The average binding energy of BenSi clusters is higher than that of pure Ben+1 clusters, indicating that the doped of the Si atom enhances the cluster's binding force. Compared with pure Ben+1 clusters, the HOMO-LUMO GAP of Be7Si, Be8Si, and Be10Si clusters increase while the HLG of other BenSi clusters(n = 1–3,5,9,11,12) decreas. The vertical ionization potential and vertical electron affinities curves of clusters have the same general trend. The VIP of the cluster decreases gradually while the VEA increases gradually. The doping of the Si atom greatly influences the stability of pure Ben clusters, and the analysis of energy and electronic properties of BenSi clusters reveals that the Be3Si cluster is the magic number structure in the system.

First-principles study of the energetics of Fe interstitial clusters in vanadium

The energetics of Fe interstitials and their clusters as well as the effect of Fe on the migration of self-interstitial (SIA) and vacancies in vanadium (V) are investigated by first-principles calculations. We determined the formation energies of mono-/di- Fe-V and Fe-Fe interstitial pairs by typical structures (<111>, <110> and <100>), and found that the <110>Fe-Fe and mixed <111>Fe-V dumbbell are the lowest energy configuration. Secondly, we determined the formation/binding energies of small Fe-Fe/Fe-V interstitial clusters with sizes of 3–6. The binding energies of clusters increase with sizes from 0.69 to 4.62 eV. The interstitial clusters tend to form three-dimensional parallel configurations and the parallel <111> configurations are the most stable. By comparison, the <111>Fe-Fe clusters are more stable than both mixed Fe-V and SIA clusters. Moreover, we explored the effect of Fe on the formation and migration of SIAs/vacancies. Fe increases defect formation energy and changes rotation barrier of SIA. The migration barrier of SIAs near Fe is still very small along <111> direction, and the SIAs near compressed Fe can transform into mixed Fe-V pair with a low barrier of 0.01 eV. Vacancy migrating towards Fe exhibits a higher barrier of 0.52/0.54 eV than that of 0.39 eV in pure V, while the barrier of vacancy exchanging Fe is very high of about 1.05 eV.

A first principles investigation of defect energetics and diffusion in actinide dioxides

In this work, we have studied the formation and migration of various neutral intrinsic defects in AnO2. The non-stoichiometric defects such as vacancy defect, interstitial defect, and antisite defect as well as stoichiometric defects such as Schottky defect and Frenkel pairs has been considered for investigation. The formation energies of point defects are much higher in ThO2 as compared to UO2 and PuO2. The binding energy of defect clusters indicate that formation of Frenkel pair and Schottky defect is favorable over individual defects in ThO2. In case of UO2 and PuO2, hyper-stoichiometric defects are more stable than hypo-stoichiometric defects. The results obtained in this work are in good agreement with experimental results.

On assessing the carbon capture performance of graphynes with particle swarm optimization.

Tackling climate change is one of the greatest challenges of current times and therefore the development of efficient technologies to limit anthropogenic emissions is of utmost urgency. Recent research towards this goal has alluded to the use of carbon-based solid sorbents for carbon capture. Graphynes (GYs), an interesting class of porous carbon membranes, have recently proven their potential as excellent membranes for gas adsorption and separation. Herein, we explored the CO2 and N2 adsorption characteristics and CO2/N2 selectivities of a class of GYs, namely γ-GY-1, γ-GY-2 and γ-GY-4. We investigated the putative global minimum geometries of adsorbed unary (n = 2-10) and binary (n : m; n, m ∈ [1, 8]) clusters of CO2 and N2 by employing a stochastic global optimization method called particle swarm optimization in conjunction with empirical intermolecular force field formulations. The intervening interactions are modeled using various pairwise potentials, including Lennard-Jones potential, improved Lennard-Jones potential, Buckingham potential and Coulombic potential. The binding energies for both unary and binary clusters are highest for adsorption on γ-GY-1, followed by γ-GY-2. The putative global minimum geometries suggested that N2 molecules preferred binding over the pore centres while CO2 molecules showed higher clustering propensity than any binding site preference. The predicted interaction energies suggested higher selectivity for CO2 over N2 for all the three γ-GYs.

Ca n neutral clusters: a two-step G 0 W 0 and DFT benchmark.

Electronic and structural properties of calcium clusters with a varying size range of 2-20 atoms are studied using a two-step scheme within the GW and density functional theory (DFT) with generalized gradient approximation (GGA). The GGA overestimates the binding energies, optimized geometries, electron affinities, and ionization potentials reported in the benchmark. The ground-state structure geometry and binding energy were obtained from the DFT for the ground-state structure of each cluster. The binding energy of the neutral clusters of the calcium series follows an increasing trend, except for a few stable even and odd clusters. The electronic properties of the calcium cluster were studied with an all-electron FHI-aims code. In the G 0 W 0 calculation, the magic cluster Ca10 has relatively high ionization potential and low electron affinity. The obtained ionization potentials from the G 0 W 0 @PBE calculation showed that the larger cluster has less variation, whereas the electron affinities of the series have an increasing trend. The ionization potentials from the G 0 W 0 benchmark for the calcium cluster series have not yet been described in the literature.

Molecular dynamics study of primary radiation damage in TiVTa concentrated solid-solution alloy

The primary radiation damage in pure V and TiVTa concentrated solid-solution alloy (CSA) was studied using a molecular dynamics method. We have performed displacement cascade simulations to explore the generation and evolution behavior of irradiation defects. The results demonstrate that the defect accumulation and agglomeration in TiVTa CSA are significantly suppressed compared to pure V. The peak value of Frenkel pairs during cascade collisions in TiVTa CSA is much higher than that in pure V due to the lower formation energy of point defects. Meanwhile, the longer lifetime of the thermal spike relaxation and slow energy dissipation capability of TiVTa CSA can facilitate the recombination of point defects. The defect agglomeration rate in TiVTa CSA is much lower due to the lower binding energy of interstitial clusters and reduced interstitial diffusivity. Furthermore, the occurrence probability of dislocation loops in TiVTa CSA is lower than that in pure V. The reduction in primary radiation damage may enhance the radiation resistance of TiVTa CSA, and the improved radiation tolerance is primarily attributed to the relaxation stage and long-term defect evolution rather than the ballistic stage. These results can provide fundamental insights into irradiation-induced defects evolution in refractory CSAs.

Molecular understanding of electron donor influences in dye-sensitized solar cells of novel series-based D-A’-(π-A)2

The efficiency of the designed dye-sensitized solar cells (DSSCs) containing phenothiazine phenoxazine, and 5,10-dimethylphenazine as donors and triazine, phenyl with D-A’-(π-A)2 architecture has been examined utilizing Time-dependent (TD-DFT) and Density Functional Theory (DFT) techniques. The geometrical structures, electrical characteristics, absorption, and photovoltaic characteristics were studied using these techniques. Additionally, the computed findings show that various layouts can alter the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) energy levels and reduce the energy gap between 1.63 and 2.30 eV. The absorption undergoes a redshift displacement. These bands are between 300 and 400 nm. This work aims at calculating the structural geometries and the electronic and optical properties of the designed dyes. In order to shed light on the bridging influence on geometric and TD-BHandH/6-31G(d) for optoelectronic properties, the density functional theory (DFT) and time-dependent TD-DFT at the B3LYP/6-31G(d) level were examined. Additionally, the complex [email protected] cluster's binding energies have been investigated.

Toward Modeling the Growth of Large Atmospheric Sulfuric Acid-Ammonia Clusters.

Studying large atmospheric molecular clusters is needed to understand the transition between clusters and aerosol particles. In this work, we studied the (SA)n(AM)n clusters with n up to 30 and the (SA)m(AM)m±2 clusters, with m = 6-20. The cluster configurations are sampled using the ABCluster program, and the cluster geometries and thermochemical parameters are calculated using GFN1-xTB. The cluster binding energies are calculated using B97-3c. We find that the addition of sulfuric acid is preferred to the addition of ammonia. The addition free energies were found to have large uncertainties, which could potentially be attributed to errors in the applied level of theory. Based on DLPNO-CCSD(T0)/aug-cc-pVTZ benchmarks of the binding energies of the large (SA)8-9(AM)10 and (SA)10(AM)10-11 clusters, we find that ωB97X-D3BJ with a large basis set is required to yield accurate binding and addition energies. However, based on recalculations of the single-point energy at r2SCAN-3c and ωB97X-D3BJ/6-311++G(3df,3pd), we show that the single-point energy contribution is not the primary source of error. We hypothesize that a larger source of error might be present in the form of insufficient configurational sampling. Finally, we train Δ machine learning model on (SA)n(AM)n clusters with n up to 5 and show that we can predict the binding energies of clusters up to sizes of (SA)30(AM)30 with a binding energy error below 0.6 %. This is an encouraging approach for accurately modeling the binding energies of large acid-base clusters in the future.

Aggregation of Size-Selected Oxide Clusters Deposited onto Au(111).

Kinetic Monte Carlo (kMC) simulations along with density functional theory (DFT) calculations were used to investigate the aggregation of size-selected Nb3Oy (y = 5, 6, 7) clusters deposited onto the Au(111) surface. Recent STM experiments showed that the cluster binding sites and sizes of the cluster assemblies on the Nb3Oy/Au(111) surfaces strongly depend on the stoichiometry of the clusters, i.e., the oxygen-to-niobium ratio. To better understand the origins of these differences, kMC simulations of the nucleation and growth of cluster assemblies were performed using energy barriers for diffusion and intercluster interactions estimated from DFT calculations of cluster binding and dimerization energies, respectively. Comparisons of the kMC simulations with STM images of the as-deposited Nb3Oy/Au(111) surfaces at RT and after high temperature annealing were used to further optimize the energetics and gauge the importance of nearest neighbor interactions. The kMC simulations demonstrate that the assembly of Nb3Oy clusters on Au(111) are largely controlled by the magnitude of the barriers for diffusion and interparticle-bond formation, while changes at higher temperatures are sensitive to the binding energies between nearest neighbors. Simulations for the Nb3O5 and Nb3O6 clusters, which exhibit smaller cluster assembly sizes in STM, required larger diffusion barriers as well as different barriers for interparticle binding, which reflected differences in DFT calculated dimerization energies. The results demonstrate the effectiveness of combined DFT and kMC calculations for understanding how the stoichiometry affects the aggregation of small oxide clusters on a metal surface.

Density Functional Theory Computation and Machine Learning Studies of Interaction between Au3 Clusters and 20 Natural Amino Acid Molecules.

The optimal adsorption sites and the binding energies of neutral Au3 clusters with 20 natural amino acids under the gas phase and water solvation were systematically investigated based on density functional theory (DFT) calculations. The calculation results showed that in the gas phase Au3 tends to bind with N atoms of amino groups in amino acids, except methionine, which tends to bind with Au3 through S atoms. Under water solvation, Au3 clusters tended to bind to N atoms of amino groups and N atoms of side chain amino groups in amino acids. However, methionine and cysteine bind more strongly to the gold atom through the S atom. Based on the binding energy data of Au3 clusters and 20 natural amino acids under water solvation calculated by DFT, a machine learning model (gradient boosted decision tree) was proposed to predict the optimal binding Gibbs free energy (ΔG) of the interaction between Au3 clusters and amino acids. The main factors affecting the strength of the interaction between Au3 and amino acids were uncovered by the feature importance analysis.

Bonding states of hydrogen for supported Ti clusters on pristine and defective graphene

To determine whether graphene-supported Ti clusters can synergistically store hydrogen through Kubas and spillover effect, we systematically investigate the growth pattern of Tin (n = 1–10) clusters on pristine and defective graphene and analyze multiple types of bonding states of hydrogen in detail. For pristine graphene, the most stable Tin (n = 1–10) clusters are the quasi-planar structure except for supported Ti4 and Ti5. The Ti dissociation energies and the binding energy of Tin clusters gradually increase with increasing n, which indicates that larger Tin clusters tend to form. Efficient spillover will occur on single-site Ti Catalysts at low hydrogen concentration due to the lower hydrogen spillover energy barrier (3.05 eV), while the energy barrier of hydrogen migration from Tin (n = 2–7) clusters to graphene on the cluster is 5.34–6.82 eV. The Ti: H ratio is a maximum of 1:8 for the single-site Ti catalyst, while decreases with the Tin cluster increases. Therefore, the pristine graphene-supported Ti nanoclusters are more suitable as substrates for hydrogen adsorbent rather than spillover. The introduced defects make Tin clusters have three-dimensional conical configurations from n = 4. Ti3 and Ti6 are the most stable clusters. Moreover, the migration energy barriers of H atoms on them decrease from 6.54 eV to 6.82 eV–4.32 eV and 3.42 eV, respectively. Our results explain recent experimental phenomena [Appl Phys Lett 2015; 106: 083,901. ACS Energy Lett 2022; 7 (7): 2297–2303] in depth at the molecular level.

STRUCTURE AND VIBRATIONS OF FREE NIN CLUSTERS (N &lt; 20)

The binding energy, equilibrium geometry, and vibration frequencies of small free Nin clusters (n &lt; 20) were calculated using interatomic interaction potentials calculated in an embedded atom method. Calculations of the energy parameter of stability АЕ2 and dissociation energy showed that the most energetically stable clusters are those with the magic numbers of atoms n = 4, 6, 13, 19. Calculations of atomic vibrations revealed that the dynamic contribution to the stability of clusters is determined by the minimum vibration frequency, whose extreme values fall on clusters with the magic numbers of atoms n = 4, 6, 13, 19. The maximum vibration frequency varies nonmonotonically and for clusters with n &lt; 19 it has no clear extreme values. This result is consistent with available experimental data on stable structures of small and medium-sized metal clusters.

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25.

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (De's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (De's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

Massive Assessment of the Binding Energies of Atmospheric Molecular Clusters.

Quantum chemical studies of the formation and growth of atmospheric molecular clusters are important for understanding aerosol particle formation. However, the search for the lowest free-energy cluster configuration is extremely time consuming. This makes high-level benchmark data sets extremely valuable in the quest for the global minimum as it allows the identification of cost-efficient computational methodologies, as well as the development of high-level machine learning (ML) models. Herein, we present a highly versatile quantum chemical data set comprising a total of 11 749 (acid)1-2(base)1-2 cluster configurations, containing up to 44 atoms. Utilizing the LUMI supercomputer, we calculated highly accurate PNO-CCSD(F12*)(T)/cc-pVDZ-F12 binding energies of the full set of cluster configurations leading to an unprecedented data set both in regard to sheer size and with respect to the level of theory. We employ the constructed benchmark set to assess the performance of various semiempirical and density functional theory methods. In particular, we find that the r2-SCAN-3c method shows excellent performance across the data set related to both accuracy and CPU time, making it a promising method to employ during cluster configurational sampling. Furthermore, applying the data sets, we construct ML models based on Δ-learning and provide recommendations for future application of ML in cluster configurational sampling.