Training atomic neural networks using fragment-based data generated in virtual reality.

The ability to understand and engineer molecular structures relies on having accurate descriptions of the energy as a function of atomic coordinates. Here, we outline a new paradigm for deriving energy functions of hyperdimensional molecular systems, which involves generating data for low-dimensional systems in virtual reality (VR) to then efficiently train atomic neural networks (ANNs). This generates high-quality data for specific areas of interest within the hyperdimensional space that characterizes a molecule's potential energy surface (PES). We demonstrate the utility of this approach by gathering data within VR to train ANNs on chemical reactions involving fewer than eight heavy atoms. This strategy enables us to predict the energies of much higher-dimensional systems, e.g., containing nearly 100 atoms. Training on datasets containing only 15k geometries, this approach generates mean absolute errors around 2 kcal mol-1. This represents one of the first times that an ANN-PES for a large reactive radical has been generated using such a small dataset. Our results suggest that VR enables the intelligent curation of high-quality data, which accelerates the learning process.

Electronic structure benchmark calculations of CO2 fixing elementary chemical steps in RuBisCO using the projector-based embedding approach.

Ribulose 1,5-bisphosphate carboxylase-oxygenase (RuBisCO) is the main enzyme involved in atmospheric carbon dioxide (CO2 ) fixation in the biosphere. This enzyme catalyzes a set of five chemical steps that take place in the same active-site within magnesium (II) coordination sphere. Here, a set of electronic structure benchmark calculations have been carried out on a reaction path proposed by Gready et al. by means of the projector-based embedding approach. Activation and reaction energies for all main steps catalyzed by RuBisCO have been calculated at the MP2, SCS-MP2, CCSD, and CCSD(T)/aug-cc-pVDZ and cc-pVDZ levels of theory. The treatment of the magnesium cation with post-HF methods is explored to determine the nature of its involvement in the mechanism. With the high-level ab initio values as a reference, we tested the performance of a set of density functional theory (DFT) exchange-correlation (xc) functionals in reproducing the reaction energetics of RuBisCO carboxylase activity on a set of model fragments. Different DFT xc-functionals show large variation in activation and reaction energies. Activation and reaction energies computed at the B3LYP level are close to the reference SCS-MP2 results for carboxylation, hydration and protonation reactions. However, for the carbon-carbon bond dissociation reaction, B3LYP and other functionals give results that differ significantly from the ab initio reference values. The results show the applicability of the projector-based embedding approach to metalloenzymes. This technique removes the uncertainty associated with the selection of different DFT xc-functionals and so can overcome some of inherent limitations of DFT calculations, complementing, and potentially adding to modeling of enzyme reaction mechanisms with DFT methods.

Interactive molecular dynamics in virtual reality from quantum chemistry to drug binding: An open-source multi-person framework.

As molecular scientists have made progress in their ability to engineer nanoscale molecular structure, we face new challenges in our ability to engineer molecular dynamics (MD) and flexibility. Dynamics at the molecular scale differs from the familiar mechanics of everyday objects because it involves a complicated, highly correlated, and three-dimensional many-body dynamical choreography which is often nonintuitive even for highly trained researchers. We recently described how interactive molecular dynamics in virtual reality (iMD-VR) can help to meet this challenge, enabling researchers to manipulate real-time MD simulations of flexible structures in 3D. In this article, we outline various efforts to extend immersive technologies to the molecular sciences, and we introduce "Narupa," a flexible, open-source, multiperson iMD-VR software framework which enables groups of researchers to simultaneously cohabit real-time simulation environments to interactively visualize and manipulate the dynamics of molecular structures with atomic-level precision. We outline several application domains where iMD-VR is facilitating research, communication, and creative approaches within the molecular sciences, including training machines to learn potential energy functions, biomolecular conformational sampling, protein-ligand binding, reaction discovery using "on-the-fly" quantum chemistry, and transport dynamics in materials. We touch on iMD-VR's various cognitive and perceptual affordances and outline how these provide research insight for molecular systems. By synergistically combining human spatial reasoning and design insight with computational automation, technologies such as iMD-VR have the potential to improve our ability to understand, engineer, and communicate microscopic dynamical behavior, offering the potential to usher in a new paradigm for engineering molecules and nano-architectures.

Exploring ultraviolet photoinduced charge-transfer dynamics in a model dinucleotide of guanine and thymine.

An understanding of the initial photoexcited states of DNA is essential to unravelling deleterious photoinduced chemical reactions and the intrinsic ultrafast photoprotection of the genetic code for all life. In our combined experimental and theoretical study, we have elucidated the primary non-radiative relaxation dynamics of a model nucleotide of guanine and thymine (2'-deoxyguanosine 3'-monophosphate 5'-thymidine, d(GpT)) in buffered aqueous solution. Experimentally, we unequivocally demonstrate that the Franck-Condon excited states of d(GpT) are significantly delocalised across both nucleobases, and mediate d(G+pT-) exciplex product formation on an ultrafast (<350 fs) timescale. Theoretical studies show that the nature of the vertical excited states is very dependent on the specific geometry of the dinucleotide, and dictate the degree of delocalised, charge-transfer or localised character. Our mechanism for prompt exciplex formation involves a rapid change in electronic structure and includes a diabatic surface crossing very close to the Franck-Condon region mediating fast d(G+pT-) formation. Exciplexes are quickly converted back to neutral ground state molecules on a ∼10 ps timescale with a high quantum yield, ensuring the photostability of the nucleotide sequence.

Training Neural Nets To Learn Reactive Potential Energy Surfaces Using Interactive Quantum Chemistry in Virtual Reality.

While the primary bottleneck to a number of computational workflows was not so long ago limited by processing power, the rise of machine learning technologies has resulted in an interesting paradigm shift, which places increasing value on issues related to data curation-that is, data size, quality, bias, format, and coverage. Increasingly, data-related issues are equally as important as the algorithmic methods used to process and learn from the data. Here we introduce an open-source graphics processing unit-accelerated neural network (NN) framework for learning reactive potential energy surfaces (PESs). To obtain training data for this NN framework, we investigate the use of real-time interactive ab initio molecular dynamics in virtual reality (iMD-VR) as a new data curation strategy that enables human users to rapidly sample geometries along reaction pathways. Focusing on hydrogen abstraction reactions of CN radical with isopentane, we compare the performance of NNs trained using iMD-VR data versus NNs trained using a more traditional method, namely, molecular dynamics (MD) constrained to sample a predefined grid of points along the hydrogen abstraction reaction coordinate. Both the NN trained using iMD-VR data and the NN trained using the constrained MD data reproduce important qualitative features of the reactive PESs, such as a low and early barrier to abstraction. Quantitative analysis shows that NN learning is sensitive to the data set used for training. Our results show that user-sampled structures obtained with the quantum chemical iMD-VR machinery enable excellent sampling in the vicinity of the minimum energy path (MEP). As a result, the NN trained on the iMD-VR data does very well predicting energies that are close to the MEP but less well predicting energies for "off-path" structures. The NN trained on the constrained MD data does better predicting high-energy off-path structures, given that it included a number of such structures in its training set.

Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution.

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wave function method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.

Multiscale analysis of enantioselectivity in enzyme-catalysed 'lethal synthesis' using projector-based embedding.

The action of fluoroacetate as a broad-spectrum mammalian pesticide depends on the 'lethal synthesis' of fluorocitrate by citrate synthase, through a subtle enantioselective enolization of fluoroacetyl-coenzyme A. In this work, we demonstrate how a projection-based embedding method can be applied to calculate coupled cluster (CCSD(T)) reaction profiles from quantum mechanics/molecular mechanics optimized pathways for this enzyme reaction. Comparison of pro-R and pro-S proton abstraction in citrate synthase at the CCSD(T)-in-DFT//MM level yields the correct enantioselectivity. We thus demonstrate the potential of projection-based embedding for determining stereoselectivity in enzymatic systems. We further show that the method is simple to apply, eliminates variability due to the choice of density functional theory functional and allows the efficient calculation of CCSD(T) quality enzyme reaction barriers.

Pushing the Limits of EOM-CCSD with Projector-Based Embedding for Excitation Energies.

The calculation of accurate excitation energies using ab initio electronic structure methods such as standard equation of motion coupled cluster singles and doubles (EOM-CCSD) has been cost prohibitive for large systems. In this work, we use a simple projector-based embedding scheme to calculate the EOM-CCSD excitation energies of acrolein solvated in water molecules modeled using density functional theory (DFT). We demonstrate the accuracy of this approach gives excitation energies within 0.01 eV of full EOM-CCSD, but with significantly reduced computational cost. This approach is also shown to be relatively invariant to the choice of functional used in the environment and allows for the description of systems with large numbers of basis functions (>1000) to be treated using state-of-the-art wave function methods. The flexibility of embedding to select orbitals to add to the excited-state method provides insights into the origins of the excitations and can reduce artifacts that could arise in traditional linear response time-dependent DFT (LR-TDDFT).

Correcting density-driven errors in projection-based embedding.

Projection-based embedding provides a simple and numerically robust framework for multiscale wavefunction-in-density-functional-theory (WF-in-DFT) calculations. The approach works well when the approximate DFT is sufficiently accurate to describe the energetics of the low-level subsystem and the coupling between subsystems. It is also necessary that the low-level DFT produces a qualitatively reasonable description of the total density, and in this work, we study model systems where delocalization error prevents this from being the case. We find substantial errors in embedding calculations on open-shell doublet systems in which self-interaction errors cause spurious delocalization of the singly occupied orbital. We propose a solution to this error by evaluating the DFT energy using a more accurate self-consistent density, such as that of Hartree-Fock (HF) theory. These so-called WF-in-(HF-DFT) calculations show excellent convergence towards full-system wavefunction calculations.

A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase.

Projector-based embedding has recently emerged as a robust multiscale method for the calculation of various electronic molecular properties. We present the coupling of projector embedding with quantum mechanics/molecular mechanics modeling and apply it for the first time to an enzyme-catalyzed reaction. Using projector-based embedding, we combine coupled-cluster theory, density-functional theory (DFT), and molecular mechanics to compute energies for the proton abstraction from acetyl-coenzyme A by citrate synthase. By embedding correlated ab initio methods in DFT we eliminate functional sensitivity and obtain high-accuracy profiles in a procedure that is straightforward to apply.

Accelerating wavefunction in density-functional-theory embedding by truncating the active basis set.

Methods where an accurate wavefunction is embedded in a density-functional description of the surrounding environment have recently been simplified through the use of a projection operator to ensure orthogonality of orbital subspaces. Projector embedding already offers significant performance gains over conventional post-Hartree-Fock methods by reducing the number of correlated occupied orbitals. However, in our first applications of the method, we used the atomic-orbital basis for the full system, even for the correlated wavefunction calculation in a small, active subsystem. Here, we further develop our method for truncating the atomic-orbital basis to include only functions within or close to the active subsystem. The number of atomic orbitals in a calculation on a fixed active subsystem becomes asymptotically independent of the size of the environment, producing the required O(N(0)) scaling of cost of the calculation in the active subsystem, and accuracy is controlled by a single parameter. The applicability of this approach is demonstrated for the embedded many-body expansion of binding energies of water hexamers and calculation of reaction barriers of SN2 substitution of fluorine by chlorine in α-fluoroalkanes.

Electronic and Magnetic Properties of Kremer's tris-Hydroxo Bridged Chromium Dimer: A Challenge for DFT.

We present computations of the zero field splitting constants in a tris-hydroxo bridged chromium dimer (Kremer's dimer). A comparison is given of broken symmetry density functional theory (DFT) and multiconfigurational ab initio methods for evaluating ZFS constants. Kremer's dimer is known to be antiferromagnetically coupled, with the spin ladder order of E(S = 0) < E(S = 1) < E(S = 2) < E(S = 3). The B3LYP functional gives the order E(S = 0) < E(S = 3) < E(S = 1) < E(S = 2), and similar results are obtained for other density functionals (PBE, M06, M06-L, and TPSS). In contrast, we find that simple CASSCF calculations yield a correct spin ladder. DFT poorly reproduces the experimental D splitting values, while the CASSCF technique coupled with quasi-degenerate perturbation theory qualitatively reproduces D for all the spin states. State-optimized orbitals result in more accurate spin state energies and D values compared to state-averaged orbitals. Inclusion of spin-spin coupling is found to be essential for both the magnitude and sign of D. The rhombic splitting parameter is found to be near zero, which is comparable to experimental results for which the analysis assumed C3h symmetry.