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Thomas A. Manz
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Verstraelen et al. (J. Chem. Theory Comput. 12 (2016) 3894-3912) recently introduced a new method for partitioning the electron density of a material into constituent atoms. Their approach falls within the class of atomic population analysis methods called stockholder charge partitioning methods in which a material electron distribution is divided into overlapping atoms. The Minimal Basis Iterative Stockholder (MBIS) method proposed by Verstraelen et al. composes the pro-atom density as a sum of exponential functions, where the number of exponential functions equals that elements row in the Periodic Table. Specifically, one exponential function is used for H and He, two for Li through Ne, three for Na through Ar, etc. In the MBIS method, the exponential functions parameters defining the pro-atom density are optimized in a self-consistent iterative procedure. Close examination reveals some important anomalies in the article by Verstaelen et al. The purpose of this comment article is to bring these important issues to readers attention and to start a discussion of them.
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An accurate force field is the key to the success of all molecular mechanics simulations on organic polymers and biomolecules. Accuracy beyond density functional theory is often needed to describe the intermolecular interactions, while most correlated wavefunction (CW) methods are prohibitively expensive for large molecules. Therefore, it posts a great challenge to develop an extendible ab initio force field for large flexible organic molecules at CW level of accuracy. In this work, we face this challenge by combining the physics-driven nonbonding potential with a data-driven subgraph neural network bonding model (named sGNN). Tests on polyethylene glycol polymer chains show that our strategy is highly accurate and robust for molecules of different sizes. Therefore, we can develop the force field from small molecular fragments (with sizes easily accessible to CW methods) and safely transfer it to large polymers, thus opening a new path to the next-generation organic force fields.
Given the piecewise approach to modeling intermolecular interactions for force fields, they can be difficult to parameterize since they are fit to data like total energies that only indirectly connect to their separable functional forms. Furthermore, by neglecting certain types of molecular interactions such as charge penetration and charge transfer, most classical force fields must rely on, but do not always demonstrate, how cancellation of errors occurs among the remaining molecular interactions accounted for such as exchange repulsion, electrostatics, and polarization. In this work we present the first generation of the (many-body) MB-UCB force field that explicitly accounts for the decomposed molecular interactions commensurate with a variational energy decomposition analysis, including charge transfer, with force field design choices that reduce the computational expense of the MB-UCB potential while remaining accurate. We optimize parameters using only single water molecule and water cluster data up through pentamers, with no fitting to condensed phase data, and we demonstrate that high accuracy is maintained when the force field is subsequently validated against conformational energies of larger water cluster data sets, radial distribution functions of the liquid phase, and the temperature dependence of thermodynamic and transport water properties. We conclude that MB-UCB is comparable in performance to MB-Pol, but is less expensive and more transferable by eliminating the need to represent short-ranged interactions through large parameter fits to high order polynomials.
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.
Kernel ridge regression (KRR) that satisfies energy conservation is a popular approach for predicting forcefield and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. However, the computational complexity of KRR increases cubically as the product of the number of atoms and simulated configurations in the training sample, due to the inversion of a large covariance matrix, which limits its applications to the simulation of small molecules. Here, we introduce the atomized force field (AFF) model that requires much less computational costs to achieve the quantum-chemical level of accuracy for predicting atomic forces and potential energies. Through a data-driven partition on the covariance kernel matrix of the force field and an induced input estimation approach on potential energies, we dramatically reduce the computational complexity of the machine learning algorithm and maintain high accuracy in predictions. The efficient machine learning algorithm extends the limits of its applications on larger molecules under the same computational budget. Using the MD17 dataset and another simulated dataset on larger molecules, we demonstrate that the accuracy of the AFF emulator ranges from 0.01-0.1 kcal mol$^{-1}$ or energies and 0.001-0.2 kcal mol$^{-1}$ $require{mediawiki-texvc}$$AA^{-1}$ for atomic forces. Most importantly, the accuracy was achieved by less than 5 minutes of computational time for training the AFF emulator and for making predictions on held-out molecular configurations. Furthermore, our approach contains uncertainty assessment of predictions of atomic forces and potentials, useful for developing a sequential design over the chemical input space, with nearly no increase of computational costs.
The BOUND program calculates the bound states of a complex formed from two interacting particles using coupled-channel methods. It is particularly suitable for the bound states of atom-molecule and molecule-molecule Van der Waals complexes and for the near-threshold bound states that are important in ultracold physics. It uses a basis set for all degrees of freedom except $R$, the separation of the centres of mass of the two particles. The Schrodinger equation is expressed as a set of coupled equations in $R$. Solutions of the coupled equations are propagated outwards from the classically forbidden region at short range and inwards from the classically forbidden region at long range, and matched at a point in the central region. Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, and rigid diatom + asymmetric top. Both programs provide an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in. With appropriate plug-in routines, BOUND can take account of the effects of external electric, magnetic and electromagnetic fields, locating bound-state energies at fixed values of the fields. The related program FIELD uses the same plug-in routines and locates values of the fields where bound states exist at a specified energy. As a special case, it can locate values of the external field where bound states cross scattering thresholds and produce zero-energy Feshbach resonances. Plug-in routines are supplied to handle the bound states of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field.
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