Accurate interaction energies by spin component scaled Möller-Plesset second order perturbation theory calculations with optimized basis sets (SCS-MP2mod): Development and application to aromatic heterocycles.

The Spin Component Scaled (SCS) MP2 method using a reduced and optimized basis set (SCS-MP2mod) is employed to compute the interaction energies of nine homodimers, formed by aromatic heterocyclic molecules (pyrrole, furan, thiophene, oxazole, isoxazole, pyridine, pyridazine, pyrimidine, and pyrazine). The coefficients of the same-spin and opposite-spin correlation energies and the Gaussian type orbitals (GTO) polarization exponents of the 6-31G** basis set are simultaneously optimized in order to minimize the energy differences with respect to the coupled-cluster with single, double and perturbative triples excitations [CCSD(T)] reference interaction energies, extrapolated to a complete basis set. It is demonstrated that the optimization of the spin scale factors leads to a noticeable improvement of the accuracy with a root mean square deviation less than 0.1 kcal/mol and a largest unsigned deviation smaller than 0.25 kcal/mol. The pyrrole dimer provides an exception, with a slightly higher deviation from the reference data. Given the high benefit in terms of computational time with respect to the CCSD(T) technique and the small loss of accuracy, the SCS-MP2mod method appears to be particularly suitable for extensive sampling of intermolecular potential energy surfaces at a quantum mechanical level. Within this framework, a transferability test of the SCS-MP2mod parameters to a benchmark set of this class of molecules is very promising as the reference interaction energies of several heterocyclic aromatic heterodimers were reproduced with a standard deviation of 0.30 kcal/mol. The SCS-MP2mod remarkably outperforms the value of 1.95 kcal/mol obtained with standard MP2/6-31G**.

An automated approach for the parameterization of accurate intermolecular force-fields: pyridine as a case study.

An automated protocol is proposed and validated, which integrates accurate quantum mechanical calculations with classical numerical simulations. Intermolecular force fields, (FF) suitable for molecular dynamics (MD) and Monte Carlo simulations, are parameterized through a novel iterative approach, fully based on quantum mechanical data, which has been automated and coded into the PICKY software, here presented. The whole procedure is tested and validated for pyridine, whose bulk phase, described through MD simulations performed with the specifically parameterized FF, is characterized by computing several of its thermodynamic, structural, and transport properties, comparing them with their experimental counterparts.

Accurate Quantum-Mechanically Derived Force-Fields through a Fragment-Based Approach: Balancing Specificity and Transferability in the Prediction of Self-Assembly in Soft Matter.

The wide range of time/length scales covered by self-assembly in soft matter makes molecular dynamics (MD) the ideal candidate for simulating such a supramolecular phenomenon at an atomistic level. However, the reliability of MD outcomes heavily relies on the accuracy of the adopted force-field (FF). The spontaneous re-ordering in liquid crystalline materials stands as a clear example of such collective self-assembling processes, driven by a subtle and delicate balance between supramolecular interactions and single-molecule flexibility. General-purpose transferable FFs often dramatically fail to reproduce such complex phenomena, for example, the error on the transition temperatures being larger than 100 K. Conversely, quantum-mechanically derived force-fields (QMD-FFs), specifically tailored for the target system, were recently shown (J. Phys. Chem. Lett.2022,13, 243) to allow for the required accuracy as they not only well reproduced transition temperatures but also yielded a quantitative agreement with the experiment on a wealth of structural, dynamic, and thermodynamic properties. The main drawback of this strategy stands in the computational burden connected to the numerous quantum mechanical (QM) calculations usually required for a target-specific parameterization, which has undoubtedly hampered the routine application of QMD-FFs. In this work, we propose a fragment-based strategy to extend the applicability of QMD-FFs, in which the amount of QM calculations is significantly reduced, being a single-molecule-optimized geometry and its Hessian matrix the only QM information required. To validate this route, a new FF is assembled for a large mesogen, exploiting the parameters obtained for two smaller liquid crystalline molecules, in this and previous work. Lengthy MD simulations are carried out with the new transferred QMD-FF, observing again a spontaneous re-orientation in the correct range of temperatures, with good agreement with the available experimental measures. The present results strongly suggest that a partial transfer of QMD-FF parameters can be invoked without a significant loss of accuracy, thus paving the way to exploit the method's intrinsic predictive capabilities in the simulation of novel soft materials.

Predicting Spontaneous Orientational Self-Assembly: In Silico Design of Materials with Quantum Mechanically Derived Force Fields.

De novo design of self-assembled materials hinges upon our ability to relate macroscopic properties to individual building blocks, thus characterizing in such supramolecular architectures a wide range of observables at varied time/length scales. This work demonstrates that quantum mechanical derived force fields (QMD-FFs) do satisfy this requisite and, most importantly, do so in a predictive manner. To this end, a specific FF, built solely based on the knowledge of the target molecular structure, is employed to reproduce the spontaneous transition to an ordered liquid crystal phase. The simulations deliver a multiscale portrait of such self-assembly processes, where conformational changes within the individual building blocks are intertwined with a 200 ns ensemble reorganization. The extensive characterization provided not only is in quantitative agreement with the experiment but also connects the time/length scales at which it was performed. Realizing QMD-FF predictive power and unmatched accuracy stands as an important leap forward for the bottom-up design of advanced supramolecular materials.

Automated Parameterization of Quantum Mechanically Derived Force Fields for Soft Materials and Complex Fluids: Development and Validation.

The reliability of molecular dynamics (MD) simulations in predicting macroscopic properties of complex fluids and soft materials, such as liquid crystals, colloidal suspensions, or polymers, relies on the accuracy of the adopted force field (FF). We present an automated protocol to derive specific and accurate FFs, fully based on ab initio quantum mechanical (QM) data. The integration of the Joyce and Picky procedures, recently proposed by our group to provide an accurate description of simple liquids, is here extended to larger molecules, capable of exhibiting more complex fluid phases. While the standard Joyce protocol is employed to parameterize the intramolecular FF term, a new automated procedure is here proposed to handle the computational cost of the QM calculations required for the parameterization of the intermolecular FF term. The latter is thus obtained by integrating the old Picky procedure with a fragmentation reconstruction method (FRM) that allows for a reliable, yet computationally feasible sampling of the intermolecular energy surface at the QM level. The whole FF parameterization protocol is tested on a benchmark liquid crystal, and the performances of the resulting quantum mechanically derived (QMD) FF were compared with those delivered by a general-purpose, transferable one, and by the third, "hybrid" FF, where only the bonded terms were refined against QM data. Lengthy atomistic MD simulations are carried out with each FF on extended 5CB systems in both isotropic and nematic phases, eventually validating the proposed protocol by comparing the resulting macroscopic properties with other computational models and with experiments. The QMD-FF yields the best performances, reproducing both phases in the correct range of temperatures and well describing their structure, dynamics, and thermodynamic properties, thus providing a clear protocol that may be explored to predict such properties on other complex fluids or soft materials.

The mechanism of the reaction between MAO and TMA: DFT study of the electronic structure and characterization of transition states for [AlOMe]6, [AlOMe]9 and [AlOMe]16 cages.

Methylaluminoxane (MAO) and trimethylaluminium (TMA) are relevant compounds in organometallic catalysis. Despite many published studies, aspects of their interaction persist an unsolved puzzle. Hence, in this work, we used quantum mechanic approaches based on density functional theory to study this topic. Our calculations revealed that interaction between MAO and TMA occurs initially by the formation of an intermediary Lewis adduct. In agreement with the latent acidity concept, the activation energy for the tensioned Al-O bond break is small, and changes with the local environment of the MAO cages. Breakage of bond belonging to two square faces requires between 4.20 and 5.80 kcal/mol, whereas square-hexagonal faces demand 0.61-9.43 kcal/mol. The products of this reaction present a terminal, acidic 3-coordinate aluminum atom, that can be capped by another TMA molecules. However, our computations suggest that entropic effects may prevent this reaction from occurring at all these sites in the MAO models studied. Additionally, we also characterize the inter/intramolecular methane elimination mechanism. These reactions are not feasible at room temperature but may occur at high temperatures.

Development and Validation of Quantum Mechanically Derived Force-Fields: Thermodynamic, Structural, and Vibrational Properties of Aromatic Heterocycles.

A selection of several aromatic molecules, representative of the important class of heterocyclic compounds, has been considered for testing and validating an automated Force Field (FF) parametrization protocol, based only on Quantum Mechanical data. The parametrization is carried out separately for the intra- and intermolecular contributions, employing respectively the Joyce and Picky software packages, previously implemented and refined in our research group. The whole approach is here automated and integrated with a computationally effective yet accurate method, devised very recently ( J. Chem. THEORY: Comput., 2018, 14, 543-556) to evaluate a large number of dimer interaction energies. The resulting quantum mechanically derived FFs are then used in extensive molecular dynamics simulations, in order to evaluate a number of thermodynamic, structural, and dynamic properties of the heterocycle's gas and liquid phases. The comparison with the available experimental data is good and furnishes a validation of the presented approach, which can be confidently exploited for the design of novel and more complex materials.

Interaction Energy Landscapes of Aromatic Heterocycles through a Reliable yet Affordable Computational Approach.

Noncovalent interactions between homodimers of several aromatic heterocycles (pyrrole, furan, thiophene, pyridine, pyridazine, pyrimidine, and pyrazine) are investigated at the ab initio level, employing the Möller-Plesset second-order perturbation theory, coupled with small Gaussian basis sets (6-31G* and 6-31G**) with specifically tuned polarization exponents. The latter are modified using a systematic and automated procedure, the MP2mod approach, based on a comparison with high level CCSD(T) calculations extrapolated to a complete basis set. The MP2mod results achieved with the modified 6-31G** basis set show an excellent agreement with CCSD(T)/CBS reference energies, with a standard deviation less than 0.3 kcal/mol. Exploiting its low computational cost, the MP2mod approach is then used to explore sections of the intermolecular energy of the considered homodimers, with the aim of rationalizing the results. It is found that the direct electrostatic interaction between the monomers electron clouds is at the origin of some observed features, and in many cases multipoles higher than dipole play a relevant role, although often the interplay with other contributions to the noncovalent forces (as for instance induction, π-π or XH-π interactions) makes a simple rationalization rather difficult.

Systematic and Automated Development of Quantum Mechanically Derived Force Fields: The Challenging Case of Halogenated Hydrocarbons.

A robust and automated protocol for the derivation of sound force field parameters, suitable for condensed-phase classical simulations, is here tested and validated on several halogenated hydrocarbons, a class of compounds for which standard force fields have often been reported to deliver rather inaccurate performances. The major strength of the proposed protocol is that all of the parameters are derived only from first principles because all of the information required is retrieved from quantum mechanical data, purposely computed for the investigated molecule. This a priori parametrization is carried out separately for the intra- and intermolecular contributions to the force fields, respectively exploiting the Joyce and Picky programs, previously developed in our group. To avoid high computational costs, all quantum mechanical calculations were performed exploiting the density functional theory. Because the choice of the functional is known to be crucial for the description of the intermolecular interactions, a specific procedure is proposed, which allows for a reliable benchmark of different functionals against higher-level data. The intramolecular and intermolecular contribution are eventually joined together, and the resulting quantum mechanically derived force field is thereafter employed in lengthy molecular dynamics simulations to compute several thermodynamic properties that characterize the resulting bulk phase. The accuracy of the proposed parametrization protocol is finally validated by comparing the computed macroscopic observables with the available experimental counterparts. It is found that, on average, the proposed approach is capable of yielding a consistent description of the investigated set, often outperforming the literature standard force fields, or at least delivering results of similar accuracy.

Accuracy of Quantum Mechanically Derived Force-Fields Parameterized from Dispersion-Corrected DFT Data: The Benzene Dimer as a Prototype for Aromatic Interactions.

A multilevel approach is presented to assess the ability of several popular dispersion corrected density functionals (M06-2X, CAM-B3LYP-D3, BLYP-D3, and B3LYP-D3) to reliably describe two-body interaction potential energy surfaces (IPESs). To this end, the automated Picky procedure ( Cacelli et al. J. Comput. Chem. 2012 , 33 , 1055 ) was exploited, which consists in parametrizing specific intermolecular force fields through an iterative approach, based on the comparison with quantum mechanical data. For each of the tested functionals, the resulting force field was employed in classical Monte Carlo and Molecular Dynamics simulations, performed on systems of up to 1000 molecules in ambient conditions, to calculate a number of condensed phase properties. The comparison of the resulting structural and dynamic properties with experimental data allows us to assess the quality of each IPES and, consequently, even the quality of the DFT functionals. The methodology is tested on the benzene dimer, commonly used as a benchmark molecule, a prototype of aromatic interactions. The best results were obtained with the CAM-B3LYP-D3 functional. Besides assessing the reliability of DFT functionals in describing aromatic IPESs, this work provides a further step toward a robust protocol for the derivation of sound force field parameters from quantum mechanical data. This method can be relevant in all those cases where standard force fields fail in giving accurate predictions.

Convergence of triples energy in CCSD(T) and CC3 calculations with correlation-consistent basis sets.

The convergence behavior of connected triples correlation energy in CCSD(T) and CC3 calculations with (aug-)cc-pVXZ basis sets has been accurately described in terms of a power law of the type E(X)=E(infinity)+AX(-4). Calculations ranging from double-Z through septuple-Z attest the validity of this X(-4) convergence model. Extrapolations generated from (X-1,X)-Z calculations yield energies of nearly (X+1)-Z quality. Typically, the fraction of triples correlation energy recovered is 0.92+/-0.05 in (D,T) extrapolations; 0.98+/-0.01 in (T,Q) extrapolations; 1.0002+/-0.0012 in (Q,5) extrapolations; and 0.9995+/-0.0005 in (5,6) extrapolations.