Using Gaussian Process Regression to Simulate the Vibrational Raman Spectra of Molecular Crystals

Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very costly, especially when dealing with response properties of materials to e.g. electric fields, which require a good description of the perturbed electronic density. In this work, we use Gaussian process regression (GPR) to predict the static polarizability and dielectric susceptibility of molecules and molecular crystals. We combine this framework with ab initio molecular dynamics to predict their anharmonic vibrational Raman spectra. We stress the importance of data representation, symmetry, and locality, by comparing the performance of different flavors of GPR. In particular, we show the advantages of using a recently developed symmetry-adapted version of GPR. As an examplary application, we choose Paracetamol as an isolated molecule and in different crystal forms. We obtain accurate vibrational Raman spectra in all cases with fewer than 1000 training points, and obtain improvements when using a GPR trained on the molecular monomer as a baseline for the crystal GPR models. Finally, we show that our methodology is transferable across polymorphic forms: we can train the model on data for one structure, and still be able to accurately predict the spectrum for a second polymorph. This procedure provides an independent route to access electronic structure properties when performing force-evaluations on empirical force-fields or machine-learned potential energy surfaces

CFD simulation of a mixing-sensitive reaction in unbaffled vessels

Stirred tanks are widely used in the process industry, often to carry out complex chemical reactions. In many of such cases the perfect mixing hypothesis is not applicable for modelling purposes, and more detailed modelling approaches are required in order to accurately describe the reactor behaviour. In this work a fully predictive modelling approach, based on Computational Fluid Dynamics, is developed. Model predictions are compared with original experimental data obtained in un unbaffled stirred vessel with a parallel-competitive, mixing sensitive reaction scheme. Notably, satisfactory results are obtained at all injection rates with no recourse to micro-mixing model, thus confirming the major role played by macro-mixing in the investigated system

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multicentered atomic basis analogous to that routinely used in density fitting approximations. However, the nonorthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex data sets, obtaining very accurate predictions using a comparatively small training set. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn–Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark data set, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy

Learning Electron Densities in the Condensed Phase

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centered auxiliary basis, which enables an accurate expansion of the all-electron density in a form suitable for learning isolated and periodic systems alike. We show that, using this formulation, the electron densities of metals, semiconductors, and molecular crystals can all be accurately predicted using symmetry-adapted Gaussian process regression models, properly adjusted for the nonorthogonal nature of the basis. These predicted densities enable the efficient calculation of electronic properties, which present errors on the order of tens of meV/atom when compared to ab initio density-functional calculations. We demonstrate the key power of this approach by using a model trained on ice unit cells containing only 4 water molecules to predict the electron densities of cells containing up to 512 molecules and see no increase in the magnitude of the errors of derived electronic properties when increasing the system size. Indeed, we find that these extrapolated derived energies are more accurate than those predicted using a direct machine-learning model. Finally, on heterogeneous data sets SALTED can predict electron densities with errors below 4%

Free surface oxygen transfer in large aspect ratio unbaffled bio-reactors, with or without draft-tube

It is widely accepted that animal cell damage in aerated bioreactors is mainly related to the bursting of bubbles at the air-liquid interface. A viable alternative to sparged bioreactors may be represented by uncovered unbaffled stirred tanks, which have been recently found to be able to provide sufficient mass transfer through the deep free surface vortex which takes place under agitation conditions. As a matter of fact, if the vortex is not allowed to reach impeller blades, no bubble formation and subsequent bursting at the free-surface, along with relevant cells damage, occurs.In this work oxygen transfer performance of large aspect ratio unbaffled stirred bioreactors, either equipped or not with an internal draft tube, is presented, in view of their use as biochemical reactors especially suited for shear sensitive cell cultivation

A Transferable Machine-Learning Model of the Electron Density

The electronic charge density plays a central role in determining the behavior of matter at the atomic scale, but its computational evaluation requires demanding electronic-structure calculations. We introduce an atom-centered, symmetry-adapted framework to machine-learn the valence charge density based on a small number of reference calculations. The model is highly transferable, meaning it can be trained on electronic-structure data of small molecules and used to predict the charge density of larger compounds with low, linear-scaling cost. Applications are shown for various hydrocarbon molecules of increasing complexity and flexibility, and demonstrate the accuracy of the model when predicting the density on octane and octatetraene after training exclusively on butane and butadiene. This transferable, data-driven model can be used to interpret experiments, initialize electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems

Mass transfer and hydrodynamic characteristics of a Long Draft Tube Self-ingesting Reactor (LDTSR) for gas-liquid-solid operations

Gas-liquid stirred vessels are widely employed to carry out chemical reactions involving a gas reagent and a liquid phase. The usual way for introducing the gas stream into the liquid phase is through suitable distributors placed below the impeller. An interesting alternative is that of using “self ingesting” vessels where the headspace gas phase is injected and dispersed into the vessel through suitable surface vortices. In this work the performance of a Long Draft Tube Self-ingesting Reactor dealing with gas-liquid-solid systems, is investigated. Preliminary experimental results on the effectiveness of this contactor for particle suspension and gas-liquid mass transfer performance in presence of solid particles are presented. It is found that the presence of low particle fractions causes a significant increase in the minimum speed required for vortex ingestion of the gas. Impeller pumping capacity and gas-liquid mass transfer coefficient are found to be affected by the presence of solid particles, though to a lesser extent than with other self-ingesting devices

Accurate molecular polarizabilities with coupled-cluster theory and machine learning

The molecular polarizability describes the tendency of a molecule to deform or polarize in response to an applied electric field. As such, this quantity governs key intra- and inter-molecular interactions such as induction and dispersion, plays a key role in determining the spectroscopic signatures of molecules, and is an essential ingredient in polarizable force fields and other empirical models for collective interactions. Compared to other ground-state properties, an accurate and reliable prediction of the molecular polarizability is considerably more difficult as this response quantity is quite sensitive to the description of the underlying molecular electronic structure. In this work, we present state-of-the-art quantum mechanical calculations of the static dipole polarizability tensors of 7,211 small organic molecules computed using linear-response coupled-cluster singles and doubles theory (LR-CCSD). Using a symmetry-adapted machine-learning based approach, we demonstrate that it is possible to predict the molecular polarizability with LR-CCSD accuracy at a negligible computational cost. The employed model is quite robust and transferable, yielding molecular polarizabilities for a diverse set of 52 larger molecules (which includes challenging conjugated systems, carbohydrates, small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy that exceeds that of hybrid density functional theory (DFT). The atom-centered decomposition implicit in our machine-learning approach offers some insight into the shortcomings of DFT in the prediction of this fundamental quantity of interest

Local gas-liquid hold-up and interfacial area via light sheet and image analysis

Particle Image Velocimetry techniques coupled with advanced Image Processing tools are receiving an increasing interest for measuring flow quantities and local bubble-size distributions in gas-liquid contactors. In this work, an effective experimental technique for measuring local gas hold-up and interfacial area, as well as bubble size distribution, is discussed. The technique, hereafter referred to as Laser Induced Fluorescence with Shadow Analysis for Bubble Sizing (LIF-SABS) is based on laser sheet illumination of the gas-liquid dispersion and synchronized camera, i.e. on equipment typically available within PIV set-ups. The liquid phase is made fluorescent by a suitable dye, and an optical filter is placed in front of the camera optics, in order to allow only fluoresced light to reach the camera CCD. In this way bubbles intercepted by the laser sheet are clearly identified thanks to the neat shade resulting in the images. This allows excluding from subsequent analysis all bubbles visible in the images but not actually intercepted by the laser sheet, so resulting in better spatial resolution and data reliability. When trying to analyze image information the problem arises that bubble sizes are generally underestimated, due to the fact that the laser sheet randomly cuts bubbles over non-diametrical planes, leading to an apparent bubble size distribution even in the ideal case of single sized bubbles. Clearly in the case of bubbles with a size distribution the experimental information obtained is affected by the superposition of effects. A statistical correction for estimating local gas hold-up and specific interfacial area from relevant apparent data as obtained by laser sheet illumination and image analysis is discussed and applied to preliminary experimental data obtained in a gas-liquid stirred vessel

Vortex shape in unbaffled stirred vessels: experimental study via digital image analysis

There is a growing interest in using unbaffled stirred tanks for addressing certain processing needs. In this work, digital image analysis coupled with a suitable shadowgraphy-based technique is used to investigate the shape of the free-surface vortex that forms in uncovered unbaffled stirred tanks. The technique is based on back-lighting the vessel and suitably averaging vortex shape over time. Impeller clearance from vessel bottom and tank filling level are varied to investigate their influence on vortex shape. A correlation is finally proposed to fully describe vortex shape also when the vortex encompasses the impeller