Atomic Orbital Energies Research Articles

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.

Electronic configurations of the d- and f-block elements follow the simple rules of energy ordering which were considered to be anomalous, previously

The existing set of principles used for the explanation of electronic configurations, has not been able to explain the electronic configurations of all the d- and f-block elements, systematically. This study proposes a new theory based on two principles, the relative decrease in the energies of the outermost atomic orbitals and the pairing energies of the electrons in different atomic orbitals for the explanation of the electronic configurations of the elements. The theory for the first time has been able to address the anomalies of the electronic configurations of the all the d- and f-block elements, systematically.

Optical and electronic properties enhancement via chalcogenides: promising materials for DSSC applications

Comparatively, metal-free sensitizers featuring the chalcogen family receive less attention despite known electronic properties for metal-chalcogenide materials. This work reports an array of optoelectronic properties using quantum chemical methods. Observed red-shifted bands within the UV/Vis to NIR regions with absorption maxima > 500nm were consistent with increasing chalcogenide size. There is a monotonic down-shift in the LUMO and ESOP energy consistent with O 2p, S 3p, Se 4p, to Te 5p atomic orbital energies. Excited-state lifetime and charge injection free energies follow the decreasing order of chalcogenide electronegativity. Adsorption energies of dyes on TiO2 anatase (101) range between - 0.08 and - 0.77eV. Based on evaluated properties, selenium- and tellurium-based materials show potential use in DSSCs and futuristic device applications. Therefore, this work motivates continued investigation of the chalcogenide sensitizers and their application. The geometry optimization was performed at B3LYP/6-31 + G(d,p) and B3LYP/LANL2DZ level of theory for lighter and heavier atoms, respectively, using Gaussian 09. The equilibrium geometries were confirmed by the absence of imaginary frequencies. Electronic spectra were obtained at CAM-B3LYP/6-31G + (d,p)/LANL2DZ level of theory. Adsorption energies for dyes on a 4 × 5 supercell TiO2 anatase (101) were obtained using VASP. The dye-TiO2 optimizations were employed using GGA and PBE with the PAW pseudo-potentials. The energy cutoff was set at 400eV and convergence threshold for self-consistent iteration was set to 10-4, and van der Waals were accounted using DFT-D3 model and on-site Coulomb repulsion potential set at 8.5eV for Ti.

Topological alloy engineering and locally linearized gap dependence on concentration

Alloy engineering is a well-established approach to tune various materials' properties, but its application to topological alloys remains rudimentary. Of special interest is the band gap, the most defining property of topological materials; however, the concentration dependence of energy gaps in topological alloys remains unknown. Here we systematically investigate the band gap evolution of a topological alloy as a function of alloy concentration, using $\mathrm{KZn}{\mathrm{Sb}}_{1\ensuremath{-}\mathrm{x}}{\mathrm{Bi}}_{\mathrm{x}}$ as a prototype, based on first-principles calculations. In contrast to the well-established smooth bowing curve for a trivial gap in semiconductor alloys, we found that the topological gap evolves generally with a complex fragmented pattern due to topological phase transitions, and most strikingly a linear dependence on concentration locally in each distinct phase. Such gap linearization is fundamentally rooted in the linear dependence on alloy concentration of spin-orbit coupling (SOC) that predominantly determines a topological gap. Furthermore, we demonstrate topological alloy engineering as a general approach to tune the topological order by modulating the band edge composition and degeneracy through the alloying-induced interplay of SOC and atomic orbital on-site energy, while the linear gap dependence on alloy concentration remains independent of the degree of topological order.

Conceptual Challenges Exhibited by Naı̈ve Undergraduate Students in the Context of Atomic Orbital Energy Diagrams

Conceptual Challenges Exhibited by Naı̈ve Undergraduate Students in the Context of Atomic Orbital Energy Diagrams

On the highest oxidation states of the actinoids in AnO4 molecules (An=Ac - Cm): A DMRG-CASSCF study.

Actinoid tetroxide molecules AnO4 (An=Ac - Cm) are investigated with the ab initio density matrix renormalization group (DMRG) approach. Natural orbital shapes are used to read out the oxidation state (OS) of the f-elements, and the atomic orbital energies and radii are used to explain the trends. The highest OSs reveal a "volcano"-type variation: For An=Ac - Np, the OSs are equal to the number of available valence electrons, that is, AcIII , ThIV , PaV , UVI , and NpVII . Starting with plutonium as the turning point, the highest OSs in the most stable AnO4 isomers then decrease as PuV , AmV , and CmIII , indicating that the 5f-electrons are hard to be fully oxidized off from Pu onward. The variations are related to the actinoid contraction and to the 5f-covalency characteristics. Combined with previous work on OSs, we review their general trends throughout the periodic table, providing fundamental understanding of OS-relevant phenomena.

Ring-opening polymerization of l-lactide catalyzed by food sweetener saccharin with organic base mediated: A computational study

The mechanisms of ring-opening polymerization (ROP) of l-lactide (L-LA) and trimethylene carbonate (TMC) by DMAP/Sac (saccharin) were disclosed by DFT calculations. The DMAP/Sac as a bifunctional catalyst can simultaneously activate monomer and initiator/chain-end in the ROPs of L-LA and TMC, respectively. And, two possible intramolecular H-bond rearrangements and two ring-opening modes were found. In addition, we computationally designed a novel two-component organocatalyst Adenine/Sac and assessed its catalytic performance. It was found that the energy barriers of rate-controlling step (ring-opening of L-LA and TMC) by Adenine/Sac apparently decrease, thus suggesting higher catalytic activity. Further analysis confirmed that the natural atomic orbital energy of N atom (E(NAO)N) in protonated Adenine is lower than that in DMAPH+, which makes the proton transfer between the protonated Adenine and monomers easier. Therefore, the present work could provide some valuable information for designing new two-component organocatalysts for ROP of cyclic esters.

Electrical properties of ZnO/<inline-formula><tex-math id="Z-20220101164636">\begin{document}${\boldsymbol{\beta}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20210635_Z-20220101164636.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20210635_Z-20220101164636.png"/></alternatives></inline-formula>-Bi<sub>2</sub>O<sub>3</sub> interfaces featuring aggregation defect under external electric fields

The safe operation of power equipment largely depends on the overvoltage protection level of the arrester. The ZnO varistors are widely used as the core components of the arresters in power systems because of the excellent nonlinear volt-ampere characteristics. In order to study the electrical properties of ZnO varistors under different external electric fields from the microstructure, the method of first-principles based on density functional theory (DFT) is used, and structure of ZnO/<i>β</i>-Bi<sub>2</sub>O<sub>3</sub> interface containing zinc interstitial (Zn<sub>i</sub>) and oxygen vacancy (V<sub>o</sub>) defects is built. The results show that the V<sub>o</sub> defect migrates after full relaxation. The Zn<sub>i</sub> shifts to the interface under an external electric field. The interface energy increases rapidly after the electric field intensity has exceeded 0.1 V/Å, which means that the interaction force between the interfaces becomes larger, the distance between ZnO and <i>β</i>-Bi<sub>2</sub>O<sub>3</sub> layers decreases, and the conductivity increases rapidly. The differential charge density, work function and Bader charge analysis method are used to calculate the barrier height at the interface, which proves that the built-in electric field is an important cause ingredient responsible for the non-linear volt-ampere characteristics of ZnO varistors. The effects of atomic orbital energy level, trap energy level and energy gap on the macroscopic conductivity of ZnO varistors are analyzed by using the method of density of states analysis. In this work are analyzed the different electrical parameters of the ZnO/<i>β</i>-Bi<sub>2</sub>O<sub>3</sub> interface with aggregation defects by adjusting the intensity of the external electric field, and a new idea is provided for learning the electrical characteristics of ZnO varistors.

Relativistic local hybrid functionals and their impact on 1s core orbital energies.

In this work, we report the first relativistic density functional theory calculations using relativistic local hybrid functionals. Besides outlining the construction of relativistic local hybrid exchange within a two-component-relativistic framework based on the picture-change transformation of the density matrix and a recently developed relativistic iso-orbital indicator, we investigate the influence of two-electron-relativistic effects, using relativistic functional ingredients in local hybrid functionals, and the choice of the exchange-correlation functional on atomic 1s core orbital energies of light and heavier elements. Finally, we discuss the applicability of relativistic 1s core orbital shifts for the relativistic correction of non-relativistic 1s core excitation energies.

Perpendicular magnetocrystalline anisotropy energy (MAE) of 111-surface slab of Fe2CoAl

We have analyzed the surface stability of different orientations(111, 001, 011) of Fe2CoAl (FCA) slabs. Among all the slabs, the orientation with 111-surface is found to be most stable with minimum energy. The surface electronic and magnetic properties along with the atomic orbital resolved magnetocrystalline anisotropy energy (MAE) has been performed by using first principles density functional theory (DFT). We have reported the surface metallicity with dispersed electronic bands around the fermi energy (EF) in all the three terminals Fe/Co/Al. This may be the result of translational broken symmetry in which metallic bonds are broken with the release of free conducting electrons on the surface. We have observed the presence of both the in-plane MAE and the out-plane MAE characterized by the distribution of total MAE over an atomic sites for each Al-, Co- and Fe-terminal. The total MAE favors in-plane magnetization in case of antiferromagnetic configured Al-terminal (MAE = 0.034 meV) and Fe-terminal (0.68 meV) whereas out-plane total MAE is observed in ferromagnetic configured Co-terminal.

Atomic structures and orbital energies of 61,489 crystal-forming organic molecules

Data science and machine learning in materials science require large datasets of technologically relevant molecules or materials. Currently, publicly available molecular datasets with realistic molecular geometries and spectral properties are rare. We here supply a diverse benchmark spectroscopy dataset of 61,489 molecules extracted from organic crystals in the Cambridge Structural Database (CSD), denoted OE62. Molecular equilibrium geometries are reported at the Perdew-Burke-Ernzerhof (PBE) level of density functional theory (DFT) including van der Waals corrections for all 62 k molecules. For these geometries, OE62 supplies total energies and orbital eigenvalues at the PBE and the PBE hybrid (PBE0) functional level of DFT for all 62 k molecules in vacuum as well as at the PBE0 level for a subset of 30,876 molecules in (implicit) water. For 5,239 molecules in vacuum, the dataset provides quasiparticle energies computed with many-body perturbation theory in the G0W0 approximation with a PBE0 starting point (denoted GW5000 in analogy to the GW100 benchmark set (M. van Setten et al. J. Chem. Theory Comput. 12, 5076 (2016))).

Structural, elastic, electronic, andoptical properties of layered TiNX (X = F, Cl, Br, I) compounds: a density functional theory study

ABSTRACTTitanium nitride halides, TiNX (X = F, Cl, Br, I) in the α-phase (orthorhombic) are exciting quasi two-dimensional (2D) electronic systems exhibiting a fascinating series of electronic ground states. Pristine TiNX are semiconductors with varying energy gaps and possess attractive properties for potential applications in optoelectronics, photovoltaics, and thermoelectrics. Alkali metal intercalated TiNCl becomes superconducting at reasonably high temperature. We have revisited the electronic band structure of TiNX using density functional theory (DFT) based calculations. The atomic orbital resolved partial electronic energy densities of states are calculated together with the total density of states (TDOS). The structural and elastic properties have been investigated in details for the first time. The elastic anisotropy has been explored. The optical properties of TiNX are studied for the first time. The Debye temperatures have been calculated and the related thermal and phonon parameters are discussed. The calculated physical parameters are compared with existing theoretical and experimental results and showed fair agreement. TiNX are found to reflect electromagnetic radiation strongly in the mid ultraviolet region. The elastic properties show high degree of anisotropy. The effect of halogen atoms on various structural, elastic, electronic, and thermal properties in TiNX are also discussed in detail.

Theoretical study of the thermodynamic parameters of (CaO)n nanoclusters with n = 2–16 in the gas and solution phases: proton affinity, molecular basicity, and pKb values

Thermodynamic quantities such as proton affinity (PA) and molecular basicity (GB) for (CaO)n nanoclusters with n = 2–16 have been calculated using three computational models of the density functional theory (DFT) (Becke, 3-parameter, Lee-Yang-Parr (B3LYP), Minnesota 2006, Perdew-Wang 1991 (PW91), Coulomb attenuated method-B3LYP, and ωB97XD functionals); Moller-Plesset perturbation theory; and Hartree-Fock with the cc-PVNZ (n = D and T) basis set in the gas phase. Absolute deviation error (AAD%) indicates that obtained PA and GB values using DFT model and the B3LYP method with mean percentage errors of 0.77 and 0.90%, respectively, have the higher accuracy than the other methods and models. The values obtained for the proton affinity and gas-phase basicity of the nanoclusters were compared to experimental data reported in the literature. In order to confirm basicity properties, quantum descriptors of the molecular electrostatic potential (MEP) and valence natural atomic orbital energies (NAO) have been computed. The MEP and NAO values for species under probe display excellent correlation coefficient. The polarizable continuum model for investigating the solvents effect of water, DMSO, and benzene on the basicity of the CaO nanoclusters has been applied.

General rules of the sub-band gaps in group-IV (Si, Ge, and Sn)-doped I-III-VI2-type chalcopyrite compounds for intermediate band solar cell: A first-principles study

In this work, we have investigated Si, Ge and Sn doped at III-site(Ga or Al) in CuGaSe2, CuAlSe2, AgGaSe2, and AgAlSe2 as the candidates for intermediate band solar cell (IBSC), and demonstrated that the absolute energy levels of the intermediate band from a given group IV dopant in various Se-based chalcopyrite hosts do not show remarkable changes. This is resulted from the fact that the intermediate band originates from the same antibonding state of IV-s and Se-p states. The intermediate bands sequence of Ge∗ < Sn∗ < Si∗ from the different dopants in the same chalcopyrite host is explained by a simple model based on the atomic orbital energy and bond interaction. Furthermore, Sn-doped CuAlSe2 with the suitable main-gap and sub-gaps has been selected out as a potential candidate for IBSC, and alloying with isovalent cations to adjust to proper sub-band gaps has been demonstrated in Ge-doped (Ag,Cu)AlSe2 and Ag(Ga,Al)Se2.

Mixed-valence Compounds: AuO2 and AuS.

Mixed-valence compounds are of great interest due to their interesting properties and wide applications. Recently, gold (Au) chemistry has experienced an unprecedented development. However, Au with mixed-valence states in Au-O compounds has not been reported thus far. Here, two hitherto unknown AuO2 and AuS compounds with mixed-valence character were identified with the aid of first-principles swarm structure searching calculations. AuO2 consists of quasi-square AuO4 moiety and AuO6 octahedron in which Au shows the mixed-valence states of III and V, the first example in Au-O binary compounds. AuS contains the linear AuS2 and quasi-square AuS4 units exhibiting AuI/III mixed-valence states. The analysis of electronic property demonstrates that AuO2 and AuS are narrow band gap semiconductors with strong hybridization between Au 5d and O 2p or S 3p. With the increase of pressure, Au-O and Au-S compounds show completely different thermodynamic stabilities, resulting from distinct shifting of pressure-induced atomic orbital energy levels of O and S atoms. Our work provides an opportunity for understanding mixed-valence character in Au-O and Au-S compounds.

Designed model for the Morita–Baylis–Hillman reaction mechanism in the presence of CaO and CaO modified with ionic liquid as a solid base catalyst: a DFT and MP2 investigation

The new model for the Morita–Baylis–Hillman reaction based on the proton transfer were inquired by MP2 and DFT methods with 6-311G++(d, p) basis set combined with IEF-PCM solvent model. We focused on the reaction between acrylonitrile and benzaldehyde, catalyzed by CaO cluster and CaO modified with [Pyr][HSO4] ionic liquid. Our results indicate that in the presence of ionic liquid, the ionic liquid acts as a shuttle for the proton transfer between species in a lower energy pathway. The proton transfer step from enolate to catalyst is predicted to be the rate-limiting step for the whole process. In order to investigate the catalyst basicity, the pKa values of acrylonitrile and methyl acrylate in the presence and absence of the catalyst were measured in DMSO as a solvent. Furthermore, the proton affinities and the basicity of the CaO cluster and CaO modified with [Pyr][HSO4] ionic liquid and its components in the gas phase have been calculated at the same level of theory. Molecular electrostatic potential and valence natural atomic orbital energies in the gas phase for the catalyst have been calculated.

Solvent Basicity, A Study of Kamlet–Taft β and Gutmann DN Values Using Computationally Derived Molecular Properties

Solvent basicity is recognized as playing a major role in solvation and is included, through empirical basicity parameters, in linear free energy relationships that account for the effects of changes in solvent on chemical reactions. It is reasonable to postulate that the basicity of a solvent molecule reflects some combination of its molecular properties. In the present study, density functional calculations using the B3LYP functional, and Hartree–Fock calculations have been used to calculate the partial atomic charges (using the Hirshfeld and CM5 models), orbital energies, polarizabilities, dipole moments and quadrupolar amplitudes for over one hundred molecules for which there are experimental values for two basicity parameters, Kamlet and Taft’s hydrogen bond acceptor strength, β, and Gutmann’s donor number, DN, a measure of Lewis basicity. Regression of the experimental β and DN values against molecular descriptors reflecting the above molecular properties yields a remarkably consistent picture. For both parameters the values for alcohols and amines lie systematically off of the regression lines through the remaining compounds, which include alkanes, aromatics, halogenated alkanes and aromatics, esters, carbonates, carboxylic acids, ketones, ethers, nitriles, phosphates, sulfides and sulfates. Independent of the calculation method or method of estimating the partial atomic charges, both experimental β and DN are essentially determined by two molecular properties: the charge on the most negative atom of the molecule and the molecular orbital from which charge donation would occur. The regression results using any of the fours sets of descriptors (reflecting the two calculation methods and two methods of charge estimation) are remarkably similar for β and DN supporting the view that these are measures of the same “basicity”.

Theoretical studies of the influence of protic and aprotic ionic liquids on the basicity of CaO as a solid base catalyst

Proton affinity (PAs) and molecular basicities (GBs) of the CaO cluster and CaO modified with protic and aprotic ionic liquids in the gas phase have been calculated at the DFT/B3LYP level with a 6-311++G (d, p) basis set. The investigations of PAs and GBs in the solution phase have been studied by means of SCRF solvent effect computations using PCM solvation model for water solvent. The influence of the ILs cations and anions on the PA and GB in the gas phase and solution at the same level of theory has been investigated. We also studied the effect of [bmTr][NO3] ionic liquid on the basicity of CaO. The calculations display that this energetic ionic liquid has a high ability to improve the basicity properties of CaO. The molecular electrostatic potential (MEP), valence natural atomic orbital energies (NAO) in the gas phase have been computed.

Reliable charge assessment on encapsulated fragment for endohedral systems

A simple scheme to determine charge distribution in endohedral complexes is suggested. It is based on comparison of inner-shell atomic orbital energies of the encapsulated species to the corresponding energies in reference systems with unambiguously defined charges on X. This robust approach is applied to endohedral borospherenes X@B39, for which the conventional schemes provide in some cases quite different results. Efficiency of proposed scheme also has been proven for typical fullerene based Sc3N@C80 endohedral complex.

Segmented Contracted Error-Consistent Basis Sets of Double- and Triple-ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations.

Segmented contracted Gaussian basis sets optimized at the one-electron exact two-component (X2C) level - including a finite size model for the nucleus - are presented for elements up to Rn. These basis sets are counterparts for relativistic all-electron calculations to the Karlsruhe "def2" basis sets for nonrelativistic (H-Kr) or effective core potential based (Rb-Rn) treatments. For maximum consistency, the bases presented here were obtained from the latter by modification and reoptimization. Additionally we present extensions for self-consistent two-component calculations, required for the splitting of inner shells by spin-orbit coupling, and auxiliary basis sets for fitting the Coulomb part of the Fock matrix. Emphasis was put both on the accuracy of energies of atomic orbitals and on the accuracy of molecular properties. A large set of more than 300 molecules representing (nearly) all elements in their common oxidation states was used to assess the quality of the bases all across the periodic table.