Tell Machine Learning Potentials What They Are Needed For: Simulation-Oriented Training Exemplified for Glycine.

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PESs) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set drawn from the same distribution as the training data. Here, we systematically investigate the relationship between such test errors and the simulation accuracy with MLPs on an example of a full-dimensional, global PES for the glycine amino acid. Our results show that the errors in the test set do not unambiguously reflect the MLP performance in different simulation tasks, such as relative conformer energies, barriers, vibrational levels, and zero-point vibrational energies. We also offer an easily accessible solution for improving the MLP quality in a simulation-oriented manner, yielding the most precise relative conformer energies and barriers. This solution also passed the stringent test by diffusion Monte Carlo simulations.

MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows.

Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program package designed to leverage the power of ML to enhance typical computational chemistry simulations and to create complex workflows. This open-source package provides plenty of choice to the users who can run simulations with the command-line options, input files, or with scripts using MLatom as a Python package, both on their computers and on the online XACS cloud computing service at XACScloud.com. Computational chemists can calculate energies and thermochemical properties, optimize geometries, run molecular and quantum dynamics, and simulate (ro)vibrational, one-photon UV/vis absorption, and two-photon absorption spectra with ML, quantum mechanical, and combined models. The users can choose from an extensive library of methods containing pretrained ML models and quantum mechanical approximations such as AIQM1 approaching coupled-cluster accuracy. The developers can build their own models using various ML algorithms. The great flexibility of MLatom is largely due to the extensive use of the interfaces to many state-of-the-art software packages and libraries.

Benchmark of general-purpose machine learning-based quantum mechanical method AIQM1 on reaction barrier heights.

Artificial intelligence-enhanced quantum mechanical method 1 (AIQM1) is a general-purpose method that was shown to achieve high accuracy for many applications with a speed close to its baseline semiempirical quantum mechanical (SQM) method ODM2*. Here, we evaluate the hitherto unknown performance of out-of-the-box AIQM1 without any refitting for reaction barrier heights on eight datasets, including a total of ∼24 thousand reactions. This evaluation shows that AIQM1's accuracy strongly depends on the type of transition state and ranges from excellent for rotation barriers to poor for, e.g., pericyclic reactions. AIQM1 clearly outperforms its baseline ODM2* method and, even more so, a popular universal potential, ANI-1ccx. Overall, however, AIQM1 accuracy largely remains similar to SQM methods (and B3LYP/6-31G* for most reaction types) suggesting that it is desirable to focus on improving AIQM1 performance for barrier heights in the future. We also show that the built-in uncertainty quantification helps in identifying confident predictions. The accuracy of confident AIQM1 predictions is approaching the level of popular density functional theory methods for most reaction types. Encouragingly, AIQM1 is rather robust for transition state optimizations, even for the type of reactions it struggles with the most. Single-point calculations with high-level methods on AIQM1-optimized geometries can be used to significantly improve barrier heights, which cannot be said for its baseline ODM2* method.

Ultra-fast semi-empirical quantum chemistry for high-throughput computational campaigns with Sparrow.

Semi-empirical quantum chemical approaches are known to compromise accuracy for the feasibility of calculations on huge molecules. However, the need for ultrafast calculations in interactive quantum mechanical studies, high-throughput virtual screening, and data-driven machine learning has shifted the emphasis toward calculation runtimes recently. This comes with new constraints for the software implementation as many fast calculations would suffer from a large overhead of the manual setup and other procedures that are comparatively fast when studying a single molecular structure, but which become prohibitively slow for high-throughput demands. In this work, we discuss the effect of various well-established semi-empirical approximations on calculation speed and relate this to data transfer rates from the raw-data source computer to the results of the visualization front end. For the former, we consider desktop computers, local high performance computing, and remote cloud services in order to elucidate the effect on interactive calculations, for web and cloud interfaces in local applications, and in world-wide interactive virtual sessions. The models discussed in this work have been implemented into our open-source software SCINE Sparrow.

Interpretable Machine Learning of Two-Photon Absorption.

Molecules with strong two-photon absorption (TPA) are important in many advanced applications such as upconverted laser and photodynamic therapy, but their design is hampered by the high cost of experimental screening and accurate quantum chemical (QC) calculations. Here a systematic study is performed by collecting an experimental TPA database with ≈900 molecules, analyzing with interpretable machine learning (ML) the key molecular features explaining TPA magnitudes, and building a fast ML model for predictions. The ML model has prediction errors of similar magnitude compared to experimental and affordable QC methods errors and has the potential for high-throughput screening as additionally validated with the new experimental measurements. ML feature analysis is generally consistent with common beliefs which is quantified and rectified. The most important feature is conjugation length followed by features reflecting the effects of donor and acceptor substitution and coplanarity.

λ-DFVB(U): A hybrid density functional valence bond method based on unpaired electron density.

In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn-Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron-electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF.

Toward Chemical Accuracy in Predicting Enthalpies of Formation with General-Purpose Data-Driven Methods.

Enthalpies of formation and reaction are important thermodynamic properties that have a crucial impact on the outcome of chemical transformations. Here we implement the calculation of enthalpies of formation with a general-purpose ANI-1ccx neural network atomistic potential. We demonstrate on a wide range of benchmark sets that both ANI-1ccx and our other general-purpose data-driven method AIQM1 approach the coveted chemical accuracy of 1 kcal/mol with the speed of semiempirical quantum mechanical methods (AIQM1) or faster (ANI-1ccx). It is remarkably achieved without specifically training the machine learning parts of ANI-1ccx or AIQM1 on formation enthalpies. Importantly, we show that these data-driven methods provide statistical means for uncertainty quantification of their predictions, which we use to detect and eliminate outliers and revise reference experimental data. Uncertainty quantification may also help in the systematic improvement of such data-driven methods.

Artificial intelligence-enhanced quantum chemical method with broad applicability.

High-level quantum mechanical (QM) calculations are indispensable for accurate explanation of natural phenomena on the atomistic level. Their staggering computational cost, however, poses great limitations, which luckily can be lifted to a great extent by exploiting advances in artificial intelligence (AI). Here we introduce the general-purpose, highly transferable artificial intelligence-quantum mechanical method 1 (AIQM1). It approaches the accuracy of the gold-standard coupled cluster QM method with high computational speed of the approximate low-level semiempirical QM methods for the neutral, closed-shell species in the ground state. AIQM1 can provide accurate ground-state energies for diverse organic compounds as well as geometries for even challenging systems such as large conjugated compounds (fullerene C60) close to experiment. This opens an opportunity to investigate chemical compounds with previously unattainable speed and accuracy as we demonstrate by determining geometries of polyyne molecules-the task difficult for both experiment and theory. Noteworthy, our method's accuracy is also good for ions and excited-state properties, although the neural network part of AIQM1 was never fitted to these properties.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited.

A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.

λ-Density Functional Valence Bond: A Valence Bond-Based Multiconfigurational Density Functional Theory With a Single Variable Hybrid Parameter.

A new valence bond (VB)-based multireference density functional theory (MRDFT) method, named λ-DFVB, is presented in this paper. The method follows the idea of the hybrid multireference density functional method theory proposed by Sharkas et al. (2012). λ-DFVB combines the valence bond self-consistent field (VBSCF) method with Kohn-Sham density functional theory (KS-DFT) by decomposing the electron-electron interactions with a hybrid parameter λ. Different from the Toulouse's scheme, the hybrid parameter λ in λ-DFVB is variable, defined as a function of a multireference character of a molecular system. Furthermore, the E C correlation energy of a leading determinant is introduced to ensure size consistency at the dissociation limit. Satisfactory results of test calculations, including potential energy surfaces, bond dissociation energies, reaction barriers, and singlet-triplet energy gaps, show the potential capability of λ-DFVB for molecular systems with strong correlation.