Journal of Chemical Theory and Computation (JCTC)

Computational Protocol for the Spectral Assignment of NMR Resonances in Covalent Organic Frameworks

S. Vanlommel, S. Borgmans, C. V. Chandran, S. Radhakrishnan, P. Van der Voort, E. Breynaert, V. Van Speybroeck
Journal of Chemical Theory and Computation (JCTC)
2024
A1

Abstract 

Solid-state nuclear magnetic resonance spectroscopy is routinely used in the field of covalent organic frameworks to elucidate or confirm the structure of the synthesized samples and to understand dynamic phenomena. Typically this involves the interpretation and simulation of the spectra through the assumption of symmetry elements of the building units, hinging on the correct assignment of each line shape. To avoid misinterpretation resulting from library-based assignment without a theoretical basis incorporating the impact of the framework, this work proposes a first-principles computational protocol for the assignment of experimental spectra, which exploits the symmetry of the underlying building blocks for computational feasibility. In this way, this protocol accommodates the validation of previous experimental assignments and can serve to complement new NMR measurements.

DOI 

https://doi.org/10.1021/acs.jctc.3c01414

Managing Expectations and Imbalanced Training Data in Reactive Force Field Development: An Application to Water Adsorption on Alumina

L. Dumortier, C. Chizallet, B. Creton, T. De Bruin, T. Verstraelen
Journal of Chemical Theory and Computation (JCTC)
2024
A1

Abstract 

ReaxFF is a computationally efficient model for reactive molecular dynamics simulations that has been applied to a wide variety of chemical systems. When ReaxFF parameters are not yet available for a chemistry of interest, they must be (re)optimized, for which one defines a set of training data that the new ReaxFF parameters should reproduce. ReaxFF training sets typically contain diverse properties with different units, some of which are more abundant (by orders of magnitude) than others. To find the best parameters, one conventionally minimizes a weighted sum of squared errors over all of the data in the training set. One of the challenges in such numerical optimizations is to assign weights so that the optimized parameters represent a good compromise among all the requirements defined in the training set. This work introduces a new loss function, called Balanced Loss, and a workflow that replaces weight assignment with a more manageable procedure. The training data are divided into categories with corresponding “tolerances”, i.e., acceptable root-mean-square errors for the categories, which define the expectations for the optimized ReaxFF parameters. Through the Log-Sum-Exp form of Balanced Loss, the parameter optimization is also a validation of one’s expectations, providing meaningful feedback that can be used to reconfigure the tolerances if needed. The new methodology is demonstrated with a nontrivial parametrization of ReaxFF for water adsorption on alumina. This results in a new force field that reproduces both the rare and frequent properties of a validation set not used for training. We also demonstrate the robustness of the new force field with a molecular dynamics simulation of water desorption from a γ-Al2O3 slab model.

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DOI 

http://dx.doi.org/10.1021/acs.jctc.3c01009

DFT-Quality Adsorption Simulations in Metal–Organic Frameworks Enabled by Machine Learning Potentials

R. Goeminne, L. Vanduyfhuys, V. Van Speybroeck, T. Verstraelen
Journal of Chemical Theory and Computation (JCTC)
19, 18, 6313-6325
2023
A1

Abstract 

Nanoporous materials such as metal–organic frameworks (MOFs) have been extensively studied for their potential for adsorption and separation applications. In this respect, grand canonical Monte Carlo (GCMC) simulations have become a well-established tool for computational screenings of the adsorption properties of large sets of MOFs. However, their reliance on empirical force field potentials has limited the accuracy with which this tool can be applied to MOFs with challenging chemical environments such as open-metal sites. On the other hand, density-functional theory (DFT) is too computationally demanding to be routinely employed in GCMC simulations due to the excessive number of required function evaluations. Therefore, we propose in this paper a protocol for training machine learning potentials (MLPs) on a limited set of DFT intermolecular interaction energies (and forces) of CO2 in ZIF-8 and the open-metal site containing Mg-MOF-74, and use the MLPs to derive adsorption isotherms from first principles. We make use of the equivariant NequIP model which has demonstrated excellent data efficiency, and as such an error on the interaction energies below 0.2 kJ mol–1 per adsorbate in ZIF-8 was attained. Its use in GCMC simulations results in highly accurate adsorption isotherms and heats of adsorption. For Mg-MOF-74, a large dependence of the obtained results on the used dispersion correction was observed, where PBE-MBD performs the best. Lastly, to test the transferability of the MLP trained on ZIF-8, it was applied to ZIF-3, ZIF-4, and ZIF-6, which resulted in large deviations in the predicted adsorption isotherms and heats of adsorption. Only when explicitly training on data for all ZIFs, accurate adsorption properties were obtained. As the proposed methodology is widely applicable to guest adsorption in nanoporous materials, it opens up the possibility for training general-purpose MLPs to perform highly accurate investigations of guest adsorption.

DOI 

http://dx.doi.org/10.1021/acs.jctc.3c00495

Modeling Electronic Response Properties with an Explicit-Electron Machine Learning Potential

M. Cools-Ceuppens, J. Dambre, T. Verstraelen
Journal of Chemical Theory and Computation (JCTC)
18 (3), 1672–1691
2022
A1

Abstract 

Explicit-electron force fields introduce electrons or electron pairs as semiclassical particles in force fields or empirical potentials, which are suitable for molecular dynamics simulations. Even though semiclassical electrons are a drastic simplification compared to a quantum-mechanical electronic wave function, they still retain a relatively detailed electronic model compared to conventional polarizable and reactive force fields. The ability of explicit-electron models to describe chemical reactions and electronic response properties has already been demonstrated, yet the description of short-range interactions for a broad range of chemical systems remains challenging. In this work, we present the electron machine learning potential (eMLP), a new explicit electron force field in which the short-range interactions are modeled with machine learning. The electron pair particles will be located at well-defined positions, derived from localized molecular orbitals or Wannier centers, naturally imposing the correct dielectric and piezoelectric behavior of the system. The eMLP is benchmarked on two newly constructed data sets: eQM7, an extension of the QM7 data set for small molecules, and a data set for the crystalline β-glycine. It is shown that the eMLP can predict dipole moments, polarizabilities, and IR-spectra of unseen molecules with high precision. Furthermore, a variety of response properties, for example, stiffness or piezoelectric constants, can be accurately reproduced.

DOI 

https://doi.org/10.1021/acs.jctc.1c00978

Three-Legged Tree Tensor Networks with SU(2) and Molecular Point Group Symmetry

K. Gunst, F. Verstraete, D. Van Neck
Journal of Chemical Theory and Computation (JCTC)
15, 2996-3007
2019
A1

Abstract 

We extend the three-legged tree tensor network state (T3NS) [J.  Chem. Theory Comput. 2018, 14, 2026-2033] by including spin and the real abelian point group symmetries.  T3NS intersperses physical tensors with branching tensors.  Physical tensors have one physical index and at most two virtual indices.  Branching tensors have up to three virtual indices and no physical index. In this way, T3NS combines the low computational cost of matrix product states and their simplicity for implementing symmetries, with the better entanglement representation of tree tensor networks. By including spin and point group symmetries, more accurate calculations can be obtained with lower computational effort. We illustrate this by presenting calculations on the bis($\mu$-oxo) and $\mu-\eta^2:\eta^2$ peroxo isomers of $[\mathrm{Cu}_2\mathrm{O}_2]^{2+}$. The used implementation is available on github.

Open Access version available at UGent repository

DOI 

http://dx.doi.org/10.1021/acs.jctc.9b00071

Membrane Permeability: Characteristic Times and Lengths for Oxygen and a Simulation-Based Test of the Inhomogeneous Solubility-Diffusion Model

O. De Vos, R.M. Venable, T. Van Hecke, G. Hummer, R.W. Pastor, A. Ghysels
Journal of Chemical Theory and Computation (JCTC)
14 (7), 3811-3824
2018
A1

Abstract 

The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.

DOI 

http://dx.doi.org/10.1021/acs.jctc.8b00115

Efficient Construction of Free Energy Profiles of Breathing Metal-Organic Frameworks Using Advanced Molecular Dynamics Simulations

R. Demuynck, S.M.J. Rogge, L. Vanduyfhuys, J. Wieme, M. Waroquier, V. Van Speybroeck
Journal of Chemical Theory and Computation (JCTC)
13 (12), 5861-5873
2017
A1

Abstract 

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials.

Open Access version available at UGent repository
Gold Open Access

DOI 

http://dx.doi.org/10.1021/acs.jctc.7b01014

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes

A. Ghysels, R.M. Venable, R.W. Pastor, G. Hummer
Journal of Chemical Theory and Computation (JCTC)
13 (6), 2962-2976
2017
A1

Abstract 

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overtons rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

DOI 

http://dx.doi.org/10.1021/acs.ictc.7b00039

The Monomer Electron Density Force Field (MEDFF): A Physically Inspired Model for Non-Covalent Interactions

S. Vandenbrande, M. Waroquier, V. Van Speybroeck, T. Verstraelen
Journal of Chemical Theory and Computation (JCTC)
13 (1), 161–179
2017
A1

Abstract 

We propose a methodology to derive pairwise-additive noncovalent force fields from monomer electron densities without any empirical input. Energy expressions are based on the symmetry-adapted perturbation theory (SAPT) decomposition of interaction energies. This ensures a physically motivated force field featuring an electrostatic, exchange repulsion, dispersion, and induction contribution, which contains two types of parameters. First, each contribution depends on several fixed atomic parameters, resulting from a partitioning of the monomer electron density. Second, each of the last three contributions (exchange-repulsion, dispersion, and induction) contains exactly one linear fitting parameter. These three so-called interaction parameters in the model are initially estimated separately using SAPT reference calculations for the S66x8 database of noncovalent dimers. In a second step, the three interaction parameters are further refined simultaneously to reproduce CCSD(T)/CBS interaction energies for the same database. The limited number of parameters that are fitted to dimer interaction energies (only three) avoids ill-conditioned fits that plague conventional parameter optimizations. For the exchange repulsion and dispersion component, good results are obtained for all dimers in the S66x8 database using one single value for the associated interaction parameters. The values of those parameters can be considered universal and can also be used for dimers not present in the original database used for fitting. For the induction component such an approach is only viable for the dispersion dominated dimers in the S66x8 database. For other dimers (such as hydrogen-bonded complexes), we show that our methodology remains applicable. However, the interaction parameter needs to be determined on a case-specific basis. As an external validation:, the force field predicts interaction energies in good agreement with CCSD(T)/CBS values for dispersion dominated dimers extracted from an HIV-II protease crystal structure with a bound ligand (indinavir). Furthermore, experimental second virial coefficients of small alkanes and alkenes are well reproduced.

Open Access version available at UGent repository
Green Open Access

DOI 

http://dx.doi.org/10.1021/acs.jctc.6b00969

When is the Fukui Function Not Normalized? The Danger of Inconsistent Energy Interpolation Models in Density Functional Theory

F. Heidar-Zadeh, R.A. Miranda-Quintana, T. Verstraelen, P. Bultinck, P.W. Ayers, A. Buekenhoudt
Journal of Chemical Theory and Computation (JCTC)
12 (12), 5777–5787
2016
A1

Abstract 

When one defines the energy of a molecule with a noninteger number of electrons by interpolation of the energy values for integer-charged states, the interpolated electron density, Fukui function, and higher-order derivatives of the density are generally not normalized correctly. The necessary and sufficient condition for consistent energy interpolation models is that the corresponding interpolated electron density is correctly normalized to the number of electrons. A necessary, but not sufficient, condition for correct normalization is that the energy interpolant be a linear function of the reference energies. Consistent with this general rule, polynomial interpolation models and, in particular, the quadratic E vs N model popularized by Parr and Pearson, do give normalized densities and density derivatives. Interestingly, an interpolation model based on the square root of the electron number also satisfies the normalization constraints. We also derive consistent least-norm interpolation models. In contrast to these models, the popular rational and exponential forms for E vs N do not give normalized electron densities and density derivatives.

DOI 

http://dx.doi.org/10.1021/acs.jctc.6b00494

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