Pictures of molecular orbitals.
Molecular orbital electron charge density pictures, noting representation close to Hartree-Fock calculation method
MOLECULAR ORBIT↗
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The importance of correlation in the molecular orbital picture
The molecular orbital picture plays a fundamental role in analyzing and interpreting the electronic structure of atoms and molecules. Evaluation of molecular orbitals obtained from the Hartree–Fock method and other one-electron Hamiltonian models is routine for quantum-chemical studies. Although these analyses have proven to be useful for identifying different patterns in electronic structure and reactivity, in many cases, the chosen set of orbitals do not incorporate many of the fundamental electron correlation effects needed to accurately describe the atom or molecule under study. This work addresses the question of whether or not the inclusion of electron correlation is essential for the orbital picture by contrasting the differences between canonical Hartree–Fock orbitals and the correlated, normalized Dyson orbitals.
Hernandez Corzo, Hector↗
Analytical gradients for molecular-orbital-based machine learning
We report molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Discovery of correlated electron molecular orbital materials using graph representations
Correlated electron molecular orbital (CEMO) materials host emergent electronic states built from molecular orbitals localized over clusters of transition metal ions yet have historically been discovered sporadically and generally been treated as isolated case studies. Here we establish CEMO materials as a systematically discoverable class and introduce a graph-based framework to identify, classify, and organize transition-metal cluster motifs in inorganic solids. Starting from crystal structures in the Materials Project, we construct transition metal connectivity graphs, extract cluster motifs using a bond-cutting algorithm, and determine cluster point groups, effective cluster sublattice dimensionality, and translational symmetry. Applying this approach in a high-throughput screen of 34,548 compounds yields 5,306 cluster-containing materials, including 2,627 stable or metastable compounds with isolated clusters and 984 materials featuring mixed-metal clusters. The resulting dataset reveals symmetry and element dependent trends in cluster formation. By integrating cluster classification with flat band lattice topology and battery-relevant information, we provide further relevant information to multiple scientific communities. The accompanying open dataset, Cluster Finder software, and interactive web platform enable systematic exploration of cluster driven electronic phenomena and establish a general pathway for discovering correlated quantum materials and functional materials with cluster-based or extended metal-metal bonding in inorganic solids.
Akhond, Md. Rajbanul [Department of Chemistry, 800↗
Scalable ab initio fragmentation methods based on a truncated expansion of the non-orthogonal molecular orbital model
An alternative formulation of the non-orthogonal molecular orbital model of electronic structure theory is developed based on the expansion of the inverse molecular orbital overlap matrix. From this model, a hierarchy of ab initio fragment-based quantum chemistry methods, referred to as the nth-order expanded non-orthogonal molecular orbital methods, are developed using a minimal number of approximations, each of which is frequently employed in intermolecular interaction theory. These novel methods are compared to existing fragment-based quantum chemistry methods, and the implications of those significant differences, where they exist, between the methods developed herein and those already existing methods are examined in detail. Computational complexities and theoretical scaling are also analyzed and discussed. Future extensions for the hierarchy of methods, to account for additional intrafragment and interfragment interactions, are outlined.
Westheimer, Bryce M. (ORCID:0000000267645714)↗
Exploring a New Regime of Molecular Orbital Physics in 4d Cluster Magnets with Resonant Inelastic X-Ray Scattering
Molecular orbital systems with clusters of heavy transition metal (TM) ions are one of the most important classes of model materials for studying the interplay between local physics and effects of itinerancy. Despite a large number of candidates identified in the family of 4d TM materials, an understanding of their physics from competing microscopic energy scales is still missing. Here, we bridge this gap by reporting the first resonant inelastic x-ray scattering (RIXS) measurement on a well-known series of Ru cluster magnets with a 6H-perovskite structure Ba 3 MRu 2 O 9 (M 3+ = In 3+ , Y 3+ , La 3+ ) comprised of Ru dimers. In addition to providing a microscopic explanation for their anomalous magnetic properties, our RIXS measurements combined with theoretical modeling uncover a new regime of molecular orbital physics where the combined effect of large hopping and small spin-orbit coupling results in highly fragile electronic states in the Ru-dimer compounds directly manifested as an abrupt change in the RIXS spectrum accompanying a tiny change in the local structure tuned by the M-site ion. This unique combination of energy scales found only in the 4d but not the 5d cluster magnets highlights the value of these materials as a new platform for studying quantum phase transition involving molecular orbitals.
36 MATERIALS SCIENCE↗
Pyrite oxidation and reduction - Molecular orbital theory considerations
In this paper, molecular orbital theory is used to explain a heterogeneous reaction mechanism for both pyrite oxidation and reduction. The mechanism demonstrates that the oxidation of FeS2 by Fe(3+) may occur as a result of three important criteria: (1) the presence of a suitable oxidant having a vacant orbital (in case of liquid phase) or site (solid phase) to bind to the FeS2 via sulfur; (2) the initial formation of a persulfido (disulfide) bridge between FeS2 and the oxidant, and (3) an electron transfer from a pi(asterisk) orbital in S2(2-) to a pi or pi(asterisk) orbital of the oxidant.
Luther, George W., III↗
Slater screening constants in atomic and molecular orbitals
Slater screening constants in atomic and molecular orbitals
PERTURBATION THEORY↗
Pictures of Molecular Orbitals
Quantum mechanical concepts and charge density of molecular orbitals
MOLECULAR STRUCTURE↗
Molecular orbital symmetry-driven trimer formation in Kagome correlated electron materials
Correlated electron materials with molecular orbital states extending over transition metal clusters can host multiferroicity, spin frustration, and unconventional insulating phases. However, the fundamental criteria that govern cluster formation and stability remain unclear. Here, we identify a symmetry, correlation, and electron-filling-driven criteria that stabilize triangular metal trimers in materials displaying transition metal Kagome patterns. Using density functional theory and chemical bonding analysis, we show that trimer formation emerges when 6–8 electrons occupy molecular orbitals derived from transition metal d-states, achieving near-complete filling of bonding states while avoiding antibonding occupation, and correlations are of intermediate strength. This principle explains the stability of Nb 3 X 8 (X = Cl, Br, I), and more broadly, our findings offer a general design rule to obtain quantum materials with quantum states extended across transition metal clusters.
Kumari, Varsha [Indiana Univ., Bloomington, IN (Un↗
Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states
We report molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. The application of Nesbet’s theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different datasets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending the MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone–backbone interaction dataset to an accuracy of 0.28 kcal/mol.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Molecular-orbital model for metal-sapphire interfacial strength
Self-consistent-field X-Alpha scattered-wave cluster molecular-orbital models have been constructed for transition and noble metals (Fe, Ni, Cu, and Ag) in contact with a sapphire (Al2O3) surface. It is found that a chemical bond is established between the metal d-orbital electrons and the nonbonding 2p-orbital electrons of the oxygen anions on the Al2O3 surface. An increasing number of occupied metal-sapphire antibonding molecular orbitals explains qualitatively the observed decrease of contact shear strength through the series Fe, Ni, Cu, and Ag.
Johnson, K. H.↗
Molecular orbital theory of vanadium in the rutile structure crystals sno2, tio2 and geo2
Vanadium molecular orbital theory in rutile structure crystals
VANADIUM↗
Effect of vacuum processing on outgassing within an orbiting molecular shield
The limiting hydrogen number density in an orbiting molecular shield is highly dependent on the outgassing rates from the materials of construction for the shield, experimental apparatus, and other hardware contained within the shield. Ordinary degassing temperatures used for ultrahigh vacuum studies (less than 450 C) are not sufficient to process metals so that the contribution to the number density within the shield due to outgassing is less than the theoretically attainable level (approximately 200 per cu. cm). Pure aluminum and type 347 stainless steel were studied as candidate shield materials. Measurements of their hydrogen concentration and diffusion coefficients were made, and the effects of high temperature vacuum processing (greater than 600 C) on their resulting outgassing rates was determined. The densities in a molecular shield due to the outgassing from either metal were substantially less ( 0.003) than the density due to the ambient atomic hydrogen flux at an orbital altitude of 500 km.
Outlaw, R. A.↗
Molecular orbitals and inner-electron-shell chemical shifts for sulfur and chlorine oxy- anions.
Chemical effects in X-ray spectra and inner shell photoelectron spectra of sulfur- and chlorine- oxygen anions and molecular orbital method
MOLECULAR ORBIT↗
Magnetic molecular orbitals in MnSi
A large body of knowledge about magnetism is attained from models of interacting spins, which usually reside on magnetic ions. Proposals beyond the ionic picture are uncommon and seldom verified by direct observations in conjunction with microscopic theory. Here, using inelastic neutron scattering to study the itinerant near-ferromagnet MnSi, we find that the system’s fundamental magnetic units are interconnected, extended molecular orbitals consisting of three Mn atoms each rather than individual Mn atoms. This result is further corroborated by magnetic Wannier orbitals obtained by ab initio calculations. It contrasts the ionic picture with a concrete example and presents an unexplored regime of the spin waves where the wavelength is comparable to the spatial extent of the molecular orbitals. Our discovery brings important insights into not only the magnetism of MnSi but also a broad range of magnetic quantum materials where structural symmetry, electron itinerancy, and correlations act in concert.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems
The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree–Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. Here, the accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, R cut . R cut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small R cut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning
This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree–Fock computations. A MOB pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of MOs. The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant derivative kernel for Gaussian process regression (GPR) is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly accurate models for both dipole moments and energies on water and 14 small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering GPR scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with the literature results, MOB-ML provides the best test mean absolute errors of 4.21 mD and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110 000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗