Semiempirical Quantum Chemistry Research Articles

Dxtb-An efficient and fully differentiable framework for extended tight-binding.

Automatic differentiation (AD) emerged as an integral part of machine learning, accelerating model development by enabling gradient-based optimization without explicit analytical derivatives. Recently, the benefits of AD and computing arbitrary-order derivatives with respect to any variable were also recognized in the field of quantum chemistry. In this work, we present dxtb-an open-source, fully differentiable framework for semiempirical extended tight-binding (xTB) methods. Developed entirely in Python and leveraging PyTorch for array operations, dxtb facilitates extensibility and rapid prototyping while maintaining computational efficiency. Through comprehensive code vectorization and optimization, we essentially reach the speed of compiled xTB programs for high-throughput calculations of small molecules. The excellent performance also scales to large systems, and batch operability yields additional benefits for execution on parallel hardware. In particular, energy evaluations are on par with existing programs, whereas the speed of automatically differentiated nuclear derivatives is only 2 to 5 times slower compared to their analytical counterparts. We showcase the utility of AD in dxtb by calculating various molecular and spectroscopic properties, highlighting its capacity to enhance and simplify such evaluations. Furthermore, the framework streamlines optimization tasks and offers seamless integration of semiempirical quantum chemistry in machine learning, paving the way for physics-inspired end-to-end differentiable models. Ultimately, dxtb aims to further advance the capabilities of semiempirical methods, providing an extensible foundation for future developments and hybrid machine learning applications. The framework is accessible at https://github.com/grimme-lab/dxtb.

COMPUTER SIMULATION OF THE STRUCTURE OF SOME AZO-DERIVATIVES OF β-DIKETONES BY THE METHODS OF QUANTUM CHEMISTRY

The electronic and spatial structures of newly synthesized derivatives of β-diketones were studied based on the results of quantum chemical calculations. The properties of β-diketones with substituted phenyldiazonium chloride, namely 8 tautomers aryl derivatives of β-diketones-(E)-3-(2-(1-(dimethylamino)-1,3-dioxobutan-2-ylidene)hydrazinyl)-2-hydroxy-5-nitrobenzene sulfonic acid (H3L1) have been studied using the PM3 semi-empirical quantum chemistry method and the density functional theory (DFT) method with the B3LYP hybrid functional and 6-31+G(d,p) basis set. Energy and electronic characteristics of 8 tautomers are investigated. The effect of intramolecular hydrogen bonding on the structure of the investigated compounds has been studied. The formation of hydrogen bonds was confirmed by Natural Bond Orbital (NBO) analysis. Theoretical studies using the PM3 and DFT methods confirm the practical conclusions about the superiority of the hydrazone form in real samples.

Preparation, Characterization, Dielectric Properties, and AC Conductivity of Chitosan Stabilized Metallic Oxides CoO and SrO: Experiments and Tight Binding Calculations.

Polymeric films made from chitosan (CS) doped with metal oxide (MO = cobalt (II) oxide and strontium oxide) nanoparticles at different concentrations (5, 10, 15, and 20% wt. MO/CS) were fabricated with the solution cast method. FTIR, SEM, and XRD spectra were used to study the structural features of those nanocomposite films. The FTIR spectra of chitosan showed the main characteristic peaks that are usually present, but they were shifted considerably by the chemical interaction with metal oxides. FTIR analysis of the hybrid chitosan-CoO nanocomposite exhibited notable peaks at 558 and 681 cm-1. Conversely, the FTIR analysis of the chitosan-SrO composite displayed peaks at 733.23 cm-1, 810.10 cm-1, and 856.39 cm-1, which can be attributed to the bending vibrations of Co-O and Sr-O bonds, respectively. In addition, the SEM graphs showed a noticeable morphological change on the surface of chitosan, which may be due to surface adsorption with metal oxide nanoparticles. The XRD pattern also revealed a clear change in the crystallinity of chitosan when it is in contact with metal oxide nanoparticles. The presence of characteristic signals for cobalt (Co) and strontium (Sr) are clearly shown in the EDX examinations, providing convincing evidence for their incorporation into the chitosan matrix. Moreover, the stability of the nanoparticle-chitosan coordinated bonding was verified from the accurate and broadly parametrized semi-empirical tight-binding quantum chemistry calculation. This leads to the determination of the structures' chemical hardness as estimated from the frontier's orbital calculations. We characterized the dielectric properties in terms of the real and imaginary dielectric permittivity as a function of frequency. Dielectric findings reveal the existence of extensive interactions of CoO and SrO, more pronounced for SrO, with the functional groups of CS through coordination bonding. This induces the charge transfer of the complexes between CoO and SrO and the CS chains and a decrease in the amount of the crystalline phase, as verified from the XRD patterns.

Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results.

Quantum chemistry provides chemists with invaluable information, but the high computational cost limits the size and type of systems that can be studied. Machine learning (ML) has emerged as a means to dramatically lower the cost while maintaining high accuracy. However, ML models often sacrifice interpretability by using components such as the artificial neural networks of deep learning that function as black boxes. These components impart the flexibility needed to learn from large volumes of data but make it difficult to gain insight into the physical or chemical basis for the predictions. Here, we demonstrate that semiempirical quantum chemical (SEQC) models can learn from large volumes of data without sacrificing interpretability. The SEQC model is that of density-functional-based tight binding (DFTB) with fixed atomic orbital energies and interactions that are one-dimensional functions of the interatomic distance. This model is trained to ab initio data in a manner that is analogous to that used to train deep learning models. Using benchmarks that reflect the accuracy of the training data, we show that the resulting model maintains a physically reasonable functional form while achieving an accuracy, relative to coupled cluster energies with a complete basis set extrapolation (CCSD(T)*/CBS), that is comparable to that of density functional theory (DFT). This suggests that trained SEQC models can achieve a low computational cost and high accuracy without sacrificing interpretability. Use of a physically motivated model form also substantially reduces the amount of ab initio data needed to train the model compared to that required for deep learning models.

Guanine Functionalization of SWCNTs Using Metalloporphyrin Photosensitizers

Chemical modifications of single-wall carbon nanotubes (SWCNT) have opened new areas in the creation of quantum defects and the tailoring of optical properties for these one-dimensional semiconducting materials. Recent research has revealed a novel and controllable chemical functionalization reaction in which guanine nucleobases of ssDNA coatings react covalently with the SWCNT side wall in the presence of singlet oxygen. Generation of singlet oxygen through photosensitizer optical excitation is a key part of this process. To further explore guanine functionalization of SWCNTs, we have investigated reaction kinetics under various conditions. We replaced the rose bengal photosensitizer by metalloporphyrin dyes. These have greater photostability and more intense and shorter wavelength absorptions, allowing them to be used at micro- to nanomolar concentrations and leaving a wider spectral transparency window for reaction monitoring. Excitation was at 405 nm. Our kinetic studies show that the rates of change of E11 and E22 energies depend linearly on sensitizer concentration, which implies that guanine functionalization is a first order reaction with respect to singlet oxygen. Using a series of oligos with the same length but different guanine contents, we find E11 spectral shifts that increase sub-linearly to an asymptotic value. To help understand the structure of the guanine covalent adduct, we also performed semi-empirical quantum chemistry simulations. These suggest that the lowest energy structure is bonded to two adjacent carbon atoms of the SWCNT sidewall, and that reaction exothermicity is larger for smaller diameter nanotubes. Computations will also be presented for presumed intermediate adducts of guanine peroxide bonded to (6,5) SWCNTs in different orientations relative to the nanotube axis.

Deep reaction network exploration of glucose pyrolysis

Resolving the reaction networks associated with biomass pyrolysis is central to understanding product selectivity and aiding catalyst design to produce more valuable products. However, even the pyrolysis network of relatively simple [Formula: see text]-D-glucose remains unresolved due to its significant complexity in terms of the depth of the network and the number of major products. Here, a transition-state-guided reaction exploration has been performed that provides complete pathways to most significant experimental pyrolysis products of [Formula: see text]-D-glucose. The resulting reaction network involves over 31,000 reactions and transition states computed at the semiempirical quantum chemistry level and approximately 7,000 kinetically relevant reactions and transition states characterized with density function theory, comprising the largest reaction network reported for biomass pyrolysis. The exploration was conducted using graph-based rules to explore the reactivities of intermediates and an adaption of the Dijkstra algorithm to identify kinetically relevant intermediates. This simple exploration policy surprisingly (re)identified pathways to most major experimental pyrolysis products, many intermediates proposed by previous computational studies, and also identified new low-barrier reaction mechanisms that resolve outstanding discrepancies between reaction pathways and yields in isotope labeling experiments. This network also provides explanatory pathways for the high yield of hydroxymethylfurfural and the reaction pathway that contributes most to the formation of hydroxyacetaldehyde during glucose pyrolysis. Due to the limited domain knowledge required to generate this network, this approach should also be transferable to other complex reaction network prediction problems in biomass pyrolysis.

Time-dependent dielectric density functional theory predictions for excited-state molecular properties using neural networks guided by lower-level quantum chemistry

This paper discusses a neural network approach for the prediction of ground- and excited-state molecular properties. The time-dependent dielectric density functional theory was employed to handle the excited state of coumarin-152 dye. We demonstrated that lower-level quantum chemistry techniques, such as the semiempirical method and the Hartree–Fock approximations, can be used to improve the predictive performance of neural network models. The semiempirical quantum chemistry method provided excellent feature vectors (descriptors) on excited-state molecular properties in terms of computational cost and performance. In addition, a vector-based descriptor to improve molecular-force predictions is discussed.

Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation.

Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel's π-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations using standard gradient-based optimization algorithms.

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.

Δ2 machine learning for reaction property prediction.

The emergence of Δ-learning models, whereby machine learning (ML) is used to predict a correction to a low-level energy calculation, provides a versatile route to accelerate high-level energy evaluations at a given geometry. However, Δ-learning models are inapplicable to reaction properties like heats of reaction and activation energies that require both a high-level geometry and energy evaluation. Here, a Δ2-learning model is introduced that can predict high-level activation energies based on low-level critical-point geometries. The Δ2 model uses an atom-wise featurization typical of contemporary ML interatomic potentials (MLIPs) and is trained on a dataset of ∼167 000 reactions, using the GFN2-xTB energy and critical-point geometry as a low-level input and the B3LYP-D3/TZVP energy calculated at the B3LYP-D3/TZVP critical point as a high-level target. The excellent performance of the Δ2 model on unseen reactions demonstrates the surprising ease with which the model implicitly learns the geometric deviations between the low-level and high-level geometries that condition the activation energy prediction. The transferability of the Δ2 model is validated on several external testing sets where it shows near chemical accuracy, illustrating the benefits of combining ML models with readily available physical-based information from semi-empirical quantum chemistry calculations. Fine-tuning of the Δ2 model on a small number of Gaussian-4 calculations produced a 35% accuracy improvement over DFT activation energy predictions while retaining xTB-level cost. The Δ2 model approach proves to be an efficient strategy for accelerating chemical reaction characterization with minimal sacrifice in prediction accuracy.

The Accuracy of Semi-Empirical Quantum Chemistry Methods on Soot Formation Simulation

Soot molecules are hazardous compounds threatening human health. Computational chemistry provides efficient tools for studying them. However, accurate quantum chemistry calculation is costly for the simulation of large-size soot molecules and high-throughput calculations. Semi-empirical (SE) quantum chemistry methods are optional choices for balancing computational costs. In this work, we validated the performances of several widely used SE methods in the description of soot formation. Our benchmark study focuses on, but is not limited to, the validation of the performances of SE methods on reactive and non-reactive MD trajectory calculations. We also examined the accuracy of SE methods of predicting soot precursor structures and energy profiles along intrinsic reaction coordinate(s) (IRC). Finally, we discussed the spin density predicted by SE methods. The SE methods validated include AM1, PM6, PM7, GFN2-xTB, DFTB2, with or without spin-polarization, and DFTB3. We found that the shape of MD trajectory profiles, the relative energy, and molecular structures predicted by SE methods are qualitatively correct. We suggest that SE methods can be used in massive reaction soot formation event sampling and primary reaction mechanism generation. Yet, they cannot be used to provide quantitatively accurate data, such as thermodynamic and reaction kinetics ones.

Theoretical Analysis of the Adsorption of Pentachlorophenol and 6-OH-BDE-47 (6-Hydroxy-2,2’,4,4’-Tetrabromodiphenyl Ether) by Boron Nitride Nanotubes Decorated with Double-Decker Lanthanide(III) Phthalocyanine Complexes

Environmental issues have become an urgent concern, and low-cost, high-efficiency environmental remediation and energy utilization are currently high priorities. In this work, zigzag (9,0) and (18,0) boron nitride nanotubes modified by double-decker lanthanide(III) phthalocyanine complexes (BN90-LnPc2, BN180-LnPc2) were investigated by semi-empirical quantum chemistry calculations. The shorter the bond length between the nitrogen atom in the complex and the hydroxyl group of the contaminant, the greater the change in the C-O-H bond angle, implying stronger adsorption. In view of the neutral and deprotonated forms of pentachlorophenol and 6-OH-BDE-47 (6-Hydroxy-2,2’,4,4’-tetrabromodiphenyl ether), the effects of the hydrogen bond on the contaminants were significantly different. The analytical results of the HSAB reactivity descriptors and frontier molecular orbitals showed that BN180-YbPc2 performed best of all the composite systems, and the interaction with pentachlorophenol was stronger than with 6-OH-BDE-47. Furthermore, BN180-YbPc2 is beneficial as a solar-energy material, according to its electronic excitation spectrum. Ultimately, the calculated results were as expected due to the materials’ multifunctional characteristics, and the exploration of material development for specific properties will be the direction for future work.

Structural Significance of Conformational Preferences and Ribose-Ring-Puckering of Hyper Modified Nucleotide 5'-Monophosphate 2-Methylthio Cyclic N6-Threonylcarbamoyladenosine (p-ms2ct6A) Present at 37th Position in Anticodon Loop of tRNALys.

Structural significance of conformational preferences and ribose ring puckering of newly discovered hyper modified nucleotide, 5'-monophosphate 2-methylthio cyclic N6-threonylcarbamoyladenosine (p-ms2ct6A) have been investigated using quantum chemical semi-empirical RM1 and molecular dynamics simulation techniques. Automated geometry optimization of most stable structure of p-ms2ct6A has also been carried out with the help of abinitio (HF SCF, DFT) as well as semi empirical quantum chemical (RM1, AM1, PM3, and PM6) methods. Most stable structure of p-ms2ct6A is stabilized by intramolecular interactions between N(3)…HC(2'), N(1)…HC(16), O(13)…HC(15), and O(13)…HO(14). The torsion angles alpha (α) and beta (β) show the significant characteristic patterns with the involvement of intramolecular hydrogen bonding to provide stability to the p-ms2ct6A. Further, molecular dynamics simulations of p-ms2ct6A revealed the role of ribose sugar ring puckering i.e. C2'-endo and C3'-endo on the structural dynamics of ms2ct6A side chain. The modified nucleotide p-ms2ct6A periodically prefers both the C2'-endo and C3'-endo sugar with 'anti' and 'syn' conformations. This property of p-ms2ct6A could be useful to recognize the starting ANN codons. All atom explicit MD simulation of anticodon loop (ACL) of tRNALys of Bacillus subtilis containing ms2ct6A at 37th position showed the U-turn feature, base stacking ability with other adjacent bases and hydrogen bonding interactions similar to the isolated base p-ms2ct6A. The ribose sugar puckering contributes to the orientation of the side chain conformation of p-ms2ct6A. Thus, the present study could be helpful to understand the structure-function relationship of the hypermodified nucleoside, ms2ct6A in recognition of the proper codons AAA/AAG during protein biosynthesis.

Eliminating Transition State Calculations for Faster and More Accurate Reactivity Prediction in Sulfa-Michael Additions Relevant to Human Health and the Environment.

Fast and accurate computational approaches to predicting reactivity in sulfa-Michael additions are required for high-throughput screening in toxicology (e.g., predicting excess aquatic toxicity and skin sensitization), chemical synthesis, covalent drug design (e.g., targeting cysteine), and data set generation for machine learning. The kinetic glutathione chemoassay is a time-consuming in chemico method used to extract kinetic data in the form of log(kGSH) for organic electrophiles. In this work, we use density functional theory to compare the use of transition states (TSs) and enolate intermediate structures following C–S bond formation in the prediction of log(kGSH) for a diverse group of 1,4 Michael acceptors. Despite the widespread use of transition state calculations in the literature to predict sulfa-Michael reactivity, we observe that intermediate structures show much better performance for the prediction of log(kGSH), are faster to calculate, and easier to obtain than TSs. Furthermore, we show how linear combinations of atomic charges from the isolated Michael acceptors can further improve predictions, even when using inexpensive semiempirical quantum chemistry methods. Our models can be used widely in the chemical sciences (e.g., in the prediction of toxicity relevant to the environment and human health, synthesis planning, and the design of cysteine-targeting covalent inhibitors), and represent a low-cost, sustainable approach to reactivity assessment.

Development of machine learning models for the prediction of laminar flame speeds of hydrocarbon and oxygenated fuels

Laminar flame speed (LFS) is a key physicochemical property of a premixed fuel/oxidizer mixture, and is critical in the description of complex combustion phenomena. Accurate experimental measurements of LFSs for various fuels have been performed to develop and validate detailed kinetic mechanisms, which in turn are used to predict LFSs under various combustion conditions. However, such procedure is inefficient, especially in large-scale turbulent combustion modeling studies. Based on previous experimental studies of LFSs for various fuels, this work aims to develop a data-driven machine learning (ML) model for the prediction of LFSs of hydrocarbon and oxygenated fuels. Descriptors computed from semi-empirical quantum chemistry methods are used as input in ML models due to the simplicity and computational-efficiency. Pearson correlation analysis is used to select important features, and 5 descriptors are screened as the input features for ML model development. The accuracies and interpretabilities of existing 16 ML algorithms in the prediction of LFSs are compared through systematically evaluated the errors based on the differences between experimental data and model prediction. These ML models include regression trees, support vector machine regression, gaussian process regression, and ensemble trees. An efficient ML model for predicting LFSs of hydrocarbon and oxygenated fuels based on gaussian process regression algorithm is proposed, which exhibits good accuracy in predicting of LFSs for variable pressure, temperature, and equivalence ratio. The dependency of LFSs on the descriptors are also analysed. The developed ML model is fast enough for integration into large-scale computational fluid dynamics for combustion studies.

Redox Profiling of Selected Apulian Red Wines in a Single Minute.

Wine is a complex bioproduct whose chemical composition is highly variable across production regions. In order to shed light on affordable ways to promote the characterization of wines and explore the physicochemical basis of their antioxidant capacity, this work reported on the quick and easy redox profiling of selected red wines from Apulia, Italy. Therefore, an affordable and quickly performed semiempirical quantum chemistry approach, i.e., the extended Hückel method, was used to compute the bandgaps of the main phytochemical markers attributed to red wines. The findings of these calculations were then compared to an electroanalytical investigation in the form of cyclic and square-wave voltammetry, and the electric current of the redox profiles was used as the input dataset for principal component analysis. Results showcased that the semiempirical quantum chemistry calculations allowed the correlation of the bandgaps to the observed faradaic signals upon voltammetry; thereby, also providing insights on their antioxidant appeal by highlighting the feasibility of charge-transfer processes at low electric potentials. Furthermore, the principal component analysis showed that the electric current dataset gathered in a time span of 55 s allowed the appropriate separation of the samples, which hints at the possible use of quick voltammetric assays as fingerprinting tools.

Atypical adsorption of polycarboxylate superplasticizers on calcium silicate hydrate surface: Converting interaction by solvent effects

Although PCE adsorption occurrence is widely perceived to correlate to the anchoring of the carboxyl group on the PCE backbone, the understanding of the details is still insufficient. Here, we investigate the microstructural behavior of PCE adsorption with and without aqueous environments by molecular dynamics simulation and semi-empirical quantum chemistry calculation. We found that the introduction of an aqueous environment can change the mode of adsorption from strictly anchoring to atypical that the chains of PCE can sweep around the C-S-H surface. Two kinds of segments on the C-S-H surface have anchored the PCE, including Ca ions and hydroxyl. The aqueous environment alters the domination segments from Ca ions to hydroxyl. Further electronic analysis proves the weakening of bonding strength between PCE and C-S-H by solvation effects. This weakened interaction promotes the potential well of free energy away from the C-S-H surface and finally caused the atypical adsorption of PCE.

From urea to melamine cyanurate: Study of a class of thermal condensation routes for the preparation of graphitic carbon nitride

This work presents a survey of the intermediates in the well-known thermal synthesis of graphitic carbon nitride from urea. The analysis of the crystalline phases depicts a successive transformation of the precursor into different substances previously used as starting reactants, whereby melamine cyanurate arises as the ultimate precursor of a class of thermal condensation routes to obtain graphitic carbon nitride. The study of the optical properties of the synthesized materials evidences the simultaneous production of an amorphous phase with a significant presence of melon oligomers. These results are also supported by the further characterization of the materials performed using THz-TDS, FTIR, HRTEM, and XPS techniques, and by theoretical studies conducted using semi-empirical quantum chemistry methods.

PyUNIxMD: A Python-based excited state molecular dynamics package.

Theoretical/computational description of excited state molecular dynamics is nowadays a crucial tool for understanding light‐matter interactions in many materials. Here we present an open‐source Python‐based nonadiabatic molecular dynamics program package, namely PyUNIxMD, to deal with mixed quantum‐classical dynamics for correlated electron‐nuclear propagation. The PyUNIxMD provides many interfaces for quantum chemical calculation methods with commercial and noncommercial ab initio and semiempirical quantum chemistry programs. In addition, the PyUNIxMD offers many nonadiabatic molecular dynamics algorithms such as fewest‐switch surface hopping and its derivatives as well as decoherence‐induced surface hopping based on the exact factorization (DISH‐XF) and coupled‐trajectory mixed quantum‐classical dynamics (CTMQC) for general purposes. Detailed structures and flows of PyUNIxMD are explained for the further implementations by developers. We perform a nonadiabatic molecular dynamics simulation for a molecular motor system as a simple demonstration.

Photo-cycloreversion mechanism in diarylethenes revisited: A multireference quantum-chemical study at the ODM2/MRCI level.

Photoswitchable diarylethenes (DAEs), over years of intense fundamental and applied research, have been established among the most commonly chosen molecular photoswitches, often employed as controlling units in molecular devices and smart materials. At the same time, providing reliable explanation for their photophysical behavior, especially the mechanism of the photo-cycloreversion transformation, turned out to be a highly challenging task. Herein, we investigate this mechanism in detail by means of multireference semi-empirical quantum chemistry calculations, allowing, for the first time, for a balanced treatment of the static and dynamic correlation effects, both playing a crucial role in DAE photochemistry. In the course of our study, we find the second singlet excited state of double electronic-excitation character to be the key to understanding the nature of the photo-cycloreversion transformation in DAE molecular photoswitches.