Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation

Development of NOTCH, an all-electron, beyond-NDDO semiempirical method: Application to diatomic molecules

In this work, we develop a new semiempirical method, dubbed NOTCH (Natural Orbital Tied Constructed Hamiltonian). Compared to existing semiempirical methods, NOTCH is less empirical in its functional form as well as parameterization. Specifically, in NOTCH, (1) the core electrons are treated explicitly; (2) the nuclear-nuclear repulsion term is calculated analytically, without any empirical parameterization; (3) the contraction coefficients of the atomic orbital (AO) basis depend on the coordinates of the neighboring atoms, which allows the size of AOs to depend on the molecular environment, despite the fact that a minimal basis set is used; (4) the one-center integrals of free atoms are derived from scalar relativistic multireference equation-of-motion coupled cluster calculations instead of empirical fitting, drastically reducing the number of necessary empirical parameters; (5) the (AA|AB) and (AB|AB)-type two-center integrals are explicitly included, going beyond the neglect of differential diatomic overlap approximation; and (6) the integrals depend on the atomic charges, effectively mimicking the "breathing" of AOs when the atomic charge varies. For this preliminary report, the model has been parameterized for the elements H-Ne, giving only 8 empirical global parameters. Preliminary results on the ionization potentials, electron affinities, and excitation energies of atoms and diatomic molecules, as well as the equilibrium geometries, vibrational frequencies dipole moments, and bond dissociation energies of diatomic molecules, show that the accuracy of NOTCH rivals or exceeds those of popular semiempirical methods (including PM3, PM7, OM2, OM3, GFN-xTB, and GFN2-xTB) as well as the cost-effective ab initio method Hartree-Fock-3c.

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.

A specific MNDO parameterization for water

A modified neglect of differential overlap has been parameterized specifically for water and its oligomers with the addition of polarization functions on both hydrogen and oxygen, Feynman dispersion, and a slight modification of the treatment of the hydrogen nucleus. The results show that it is possible to easily obtain good geometries and energies for hydrogen-bonded water aggregates. Data from the Benchmark Energy and Geometry Database water-cluster database were used to parameterize the new Hamiltonian for water clusters from the dimer to the decamer using MP2/aug-cc-pVDZ optimized geometries and CCSD(T)/CBS oligomerization energies. Seventy five oligomerization and rearrangement energies derived from the parameterization data are reproduced with a root mean-square error (RMSE) of 0.79 kcal mol^-1 and the geometries of 38 oligomers with an RMSE of 0.17 Å. Interestingly, the Feynman dispersion term adopts a role different from that intended and tunes the atomic polarizability. The implications of these results in terms of future dedicated neglect of diatomic differential overlap Hamiltonians and those that use force-field-like atom types are discussed.

Quantum Chemistry in the Age of Machine Learning

As the quantum chemistry (QC) community embraces machine learning (ML), the number of new methods and applications based on the combination of QC and ML is surging. In this Perspective, a view of the current state of affairs in this new and exciting research field is offered, challenges of using machine learning in quantum chemistry applications are described, and potential future developments are outlined. Specifically, examples of how machine learning is used to improve the accuracy and accelerate quantum chemical research are shown. Generalization and classification of existing techniques are provided to ease the navigation in the sea of literature and to guide researchers entering the field. The emphasis of this Perspective is on supervised machine learning.

Analysis of Density Functional Tight Binding with Natural Bonding Orbitals

The description of chemical bonding by the density functional tight binding (DFTB) model is analyzed using natural bonding orbitals (NBOs) and compared to results from density functional theory (B3LYP/aug-cc-pVTZ) calculations. Several molecular systems have been chosen to represent fairly diverse bonding scenarios that include standard covalent bonds, hypervalent interactions, multicenter bonds, metal-ligand interactions (with and without the pseudo-Jahn-Teller effect), and through-space donor-acceptor interactions. Overall, the results suggest that DFTB3/3OB provides physically sound descriptions for the different bonding scenarios analyzed here, as reflected by the general agreement between DFTB3 and B3LYP NBO properties, such as the nature of the NBOs, the magnitudes of natural charges and bond orders, and the dominant donor-acceptor interactions. The degree of ligand-to-metal charge transfer and the ionic nature of pentavalent phosphate are overestimated, likely reflecting the minimal-basis nature of DFTB3/3OB. Moreover, certain orbital interactions, such as geminal interactions, are observed to be grossly overestimated by DFTB3 for hypervalent phosphate and several transition metal compounds that involve copper and nickel. The study indicates that results from NBO analysis can be instructive for identifying electronic structure descriptions at the approximate quantum-mechanical level that require improvement and thus for guiding the systematic improvement of these methods.

Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections

We present two new semiempirical quantum-chemical methods with orthogonalization and dispersion corrections: ODM2 and ODM3 (ODM x). They employ the same electronic structure model as the OM2 and OM3 (OM x) methods, respectively. In addition, they include Grimme's dispersion correction D3 with Becke-Johnson damping and three-body corrections E ABC for Axilrod-Teller-Muto dispersion interactions as integral parts. Heats of formation are determined by adding explicitly computed zero-point vibrational energy and thermal corrections, in contrast to standard MNDO-type and OM x methods. We report ODM x parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine that are optimized with regard to a wide range of carefully chosen state-of-the-art reference data. Extensive benchmarks show that the ODM x methods generally perform better than the available MNDO-type and OM x methods for ground-state and excited-state properties, while they describe noncovalent interactions with similar accuracy as OM x methods with a posteriori dispersion corrections.