Orbital Wave Functions Research Articles

Chemical information from XPS: Theory and experiment for Ni(OH)2.

The features and the electronic character of the states for the Ni 2p x-ray photoelectron spectroscopy (XPS) of Ni(OH)2 were analyzed. This detailed analysis is based on abinitio molecular orbital wavefunctions for a cluster model of Ni(OH)2. The theory is validated by comparison with experiment. Then, advanced methods are used to explain and contrast the properties of different groups of ionic states. An important conclusion is that in most cases, the ionic states cannot be described with a single configuration or determinant. Despite this essential many-body character of the XPS, we demonstrate that it is possible to understand the origin of the main and satellite XPS features in terms of their orbital character.

New definitions of the effective nuclear charge and its application to estimate the matrix element [formula omitted]

New definitions of the effective nuclear charge are proposed to evaluate the orbital wave function and the dipole matrix element ⟨n,l|r|n′,l′⟩ for the non-hydrogenic atoms or ions. It is found that the commonly used effective nuclear charge defined by the orbital energy is insufficiently precise to estimate the orbital wave functions and matrix elements ⟨n,l|r|n′,l′⟩. Instead, the effective nuclear charge defined by ⟨r⟩ or ⟨r2⟩ are more advantageous. It is shown that the effective nuclear charge method becomes increasingly precise to predict wave functions and matrix elements as the orbital angular momentum, the principle quantum number and the degree of ionization increase. Good accuracy is achieved when principal quantum numbers are identical n=n′ or when both orbital quantum numbers l and l′ are non-zero. When s-orbitals are involved (l or l′ equal to zero) the precision is decreasing.

Coherent control of rare earth 4f shell wavefunctions in the quantum spin liquid Tb2Ti2O7

The resonant excitation of electronic transitions with coherent laser sources creates quantum coherent superpositions of the involved electronic states. Most time-resolved studies have focused on gases or isolated subsystems embedded in insulating solids, aiming for applications in quantum information. Here, we focus on the coherent control of orbital wavefunctions in the correlated quantum material Tb2Ti2O7, which forms an interacting spin liquid ground state. We show that resonant excitation with a strong THz pulse creates a coherent superposition of the lowest energy Tb 4f states. The coherence manifests itself as a macroscopic oscillating magnetic dipole, which is detected by ultrafast resonant x-ray diffraction. We envision the coherent control of orbital wavefunctions demonstrated here to become a new tool for the ultrafast manipulation and investigation of quantum materials.

"Core-Shell" Wave Function Modulation in Organic Narrowband Emitters.

Efficient red-green-blue primary luminescence with an extraordinarily narrow band and durability is crucial for advanced display applications. Recently, the emergence of multiple-resonance (MR) from short-range atomic interactions has been shown to induce extremely narrow spectral widths in pure organic emitters. However, achieving wide-range color tuning without compromising color purity remains a persistent challenge for MR emitters. Herein, the concept of electronic donor/acceptor "core-shell" modulation is proposed within a boron/nitrogen (B/N) MR skeleton, enabling the rational utilization of intramolecular charge transfer to facilitate wavelength shift. The dense B atoms localized at the center of the molecule effectively compress the electron density and stabilize the lowest unoccupied molecular orbital wave function. This electron-withdrawing core is embedded with peripheral electron-donating atoms. Consequently, doping a single B atom into a deep-blue MR framework led to a profound bathochromic shift from 447 to 624 nm (∼0.8 eV) while maintaining a narrow spectral width of 0.10 eV in this pure-red emitter. Notably, organic light-emitting diodes assisted by thermally activated delayed fluorescence molecules achieved superb electroluminescent stability, with an LT99 (99% of the initial luminance) exceeding 400 h at an initial luminance of 1000 cd m-2, approaching commercial-level performance without the assistance of phosphors.

Alkaline earth metal substitutional doped C20: a density functional study

Exploring the structure and electronic properties has become a very interesting subject for nanomaterial application in many fields. This study presents a comprehensive density functional theory exploration of structure and electronic properties of alkaline earth metal (Be, Mg, and Ca) substitutional doped C20 fullerene. The study shows that MC19 (M = Be, Mg, and Ca) cage has elongated M–C bond lengths and expanded C–M–C bond angles. The Be in BeC19 gains a modest charge, while Mg in MgC19 and Ca in CaC19 donate charge. The most amazing result is that MC19 has very large energy gap, which indicates their higher stabilities than C60, and further proved by the larger hardness of MC19 than that of C20. Importantly, the physical interaction mechanism between M and the cage are different for three MC19 structures, which can be proved by the frontier orbital wavefunction and total density of states. The chemical potential values of C20 are larger than that of MC19, indicating their weaker ability to contain electrons and higher activity. Our research will provide the groundwork for rational design and application of such materials in electronic devices and nanotechnology fields. Highlights Substitutioonal doping of Be(Mg, Ca) brings remarkable influence on the geometric structure of C20. The MC19(M = Be, Mg, and Ca) has higher stability than C20. It is evident MC19(M = Be, Mg, and Ca) clusters have none magnetic moment. The chemical potential values of C20 are higher than those of MC19(M = Be, Mg, and Ca). Our research will provide the groundwork for rational design and application of such materials in electronic devices and nanotechnology fields.

Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding.

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.

Exploring the structure and dynamics of a fluorescent schiff base (1E,1′E)-1,1′-(1,4-phenylene) bis(N-(4-chlorophenyl) methamine: Synthesis, spectroscopic analysis, thermal, electronic and crystallographic study with biological applications

Schiff bases have emerged as attractive biological agents with a wide range of uses due to the extraordinary physical, chemical, and pharmacological characteristics that they possess. This study focuses on the effective synthesis of a Schiff base that is produced from 4-chloroaniline and terephthaldehyde. The success of this synthesis is supported by a variety of spectroscopic methods and Single crystal XRD analysis. The chemical that was synthesised had significant fluorescence qualities, with measured values at 457.13, 481.49, and 524.15 nm, highlighting the fact that it has the potential to be utilised in a variety of applications within the field. Using thermogravimetric analysis, the thermal stability of the compound was studied, which revealed an excellent stability at 399 °C. Thermal stability is an essential component of compound usefulness. Molecular insights were obtained by the utilisation of Density Functional Theory, which revealed an energy gap of 1.70 electron volts (eV) and electrophilic behaviour in certain atoms. The distribution of charges was brought to light through the use of Mulliken charges and molecular electrostatic potential analysis, which brought attention to the distinctive qualities of the subject molecule. An examination of the electron localization function revealed that the electron density inside carbon, nitrogen, and chlorine atoms had been delocalized. Additionally, the localised orbital locator wave function and reduced density gradient maps offered vital insights into the non-covalent interactions that were taking place within the system under investigation. In the course of the evaluation of antimicrobial efficacy, it was discovered that the chemical exhibited more powerful antibacterial activity against gram-positive B. subtilis than the conventional antibiotic amoxicillin. The antibacterial findings were further supported by molecular docking tests, which involved using particular proteins from the target species. These investigations showed that B. subtilis had a higher affinity for binding. These findings were further validated by molecular dynamic simulations. The synthesised chemical was subjected to in silico toxicity assessment using seven models, which demonstrated its non-irritating properties on the skin and eyes. The extensive analysis that is given here lays the groundwork for more targeted research on novel antibacterial drugs, with a particular focus on the safety, molecular interactions, and effectiveness of these compounds. As a result of the compound's potential applicability in biocompatible antimicrobial formulations, it is a viable candidate for improving the development of antibacterial medicines that are both effective and safe.

Theoretical approaches toward designing sensitive materials for carbon nanotube-based field-effect transistor gas sensors

Screening sensitive materials is one of the keys to designing high-performance carbon nanotube-based field-effect transistor gas sensors. Here, we proposed a reliable way (e.g., H2S) to design sensitive materials with high efficiency based on theory and experiment. Our results demonstrated that the interaction between H2S and the sensitive materials must satisfy both energy level and parity match, and the maximum overlap of the orbital wave function. Especially, the gas ΔQ exhibits a strong linear scaling with the metal φ (ΔQ∝φ). Meanwhile, Δφ will result in changes in the threshold voltage of the sensor (ΔVth∝Δφ) in experiments, which would lead to different response intensities. Therefore, the greater the ΔQ, the more changes in the threshold voltage, and corresponding higher response intensity. Expectedly, our experimental results show that the response intensity at equivalent concentrations is in high agreement with the theory (Pt > Pd > Ag), and the limit of H2S detection is low to 20 ppb.

Design of sensitive materials for nitrogen oxides detection

Although the d-band center theory can well describe the interaction between gas molecules and transition metal surfaces, the detailed reaction process and specific adsorption conditions are unclear. Hence, in this work, we systematically studied the adsorption mechanism, adsorption conditions, and recovery time of NO and NO2 molecules on different transition metals (Cu, Ag, Au, Ni, Pd, Pt, Rh, Ru, Tc, Mo, Nb, and Zr) surfaces by first-principles. The results indicated that the charge transfers from the dz2, dxz, and dyz orbitals of substrate atoms to the HOMOs/LUMOs of NO and NO2. Moreover, we demonstrate that the interaction orbitals between the NO/NO2 and the metal atoms excellently correspond with the match of energy level and parity, and the maximum overlap of the orbital wave function. Interestingly, the excellent linear scaling between charge transfer and the d-band center, work function, and matrix element (V2ad) of metals has been confirmed. Specifically, the different recovery times of these systems at different temperatures were explored. Our results can provide a feasible way for exploring gas-sensitive materials in the experiments.

Linear scaling of charge transfer versus work function of Ammonia chemisorption on X-metal (X = Ag, Au, Pd, and Pt) surface

Although the d-band center theory can efficiently describe the interaction between gas molecules and transition metal surfaces, the specific reaction process and detailed adsorption criteria remain unclear. Therefore, we systemically investigated the adsorption process and mechanism of Ammonia (NH3) molecules on transition metal (i.e., Ag, Au, Pd and Pt) surfaces using first-principles calculations. Results indicate that the NH3 molecule undergoes chemisorption on the Pt (111) surface with considerable charge transfer and adsorption energy, indicating that Pt metal is a promising NH3-sensitive material. Furthermore, the chemisorption primarily entails the highest-occupied molecular orbital (HOMO) of NH3, and the metal atoms conform perfectly to the principles of energy-level matching, wave function matching, and maximal orbital wave function overlap. Notably, a linear relationship exists between the charge transfer of NH3 and the work function of X-metal substrates. Our findings provide a feasible way to efficiently design NH3-sensitive materials for experiments.

Pd doping Au(1 1 1) surfaces enhancing formaldehyde adsorption: A first-principle study

Toxic gas detection is essential and valuable in pollution monitoring. We used first-principles computations to investigate the adsorption behavior and interaction mechanism of formaldehyde (HCHO) molecules on the Pd/Au(111) surface. The results reveal that HCHO is physisorbed on the Au(111) surface and chemisorbed on the Pd(111) surface. Furthermore, Pd atoms doped on the Au(111) surface can significantly increase the adsorption energies and charge transfers of the HCHO molecule, implying that the Pd metal can function as an excellent sensitivematerial for HCHO response. Additionally, the interaction mechanism between the HCHO molecule and the Pd atoms demonstrated that the two must meet the rules of energy-level matching and orbital wave function maximum overlap perfectly. Our research could pave the way for developing high-performance gas sensors by exploring gas-sensitive materials.

Main and Satellite Features in the Ni 2p XPS of NiO.

The origin and assignment of the complex main and satellite X-ray photoelectron spectroscopy (XPS) features of the cations in ionic compounds have been the subject of extensive theoretical studies using different methods. There is agreement that within a molecular orbital model, one needs to take into account different types of configurations. Specifically, those where a core electron is removed, but no other configuration changes are made and those where in addition to ionization, there are also shake or charge-transfer changes to the ionic configuration. However, there are strong disagreements about the assignment of XPS features to these configurations. The present work is directed toward resolving the origin of main and satellite features for the Ni 2p XPS of NiO based on ab initio molecular orbital wave functions (WFs) for a cluster model of NiO. A major problem in earlier ab initio XPS studies of ionic compounds has been the use of a common set of orbitals that was not able to properly describe all the ionic configurations that contribute to the full XPS spectra. This is resolved in the present work by using orbitals that are optimized for averages of the occupations of the different configurations that contribute to the XPS. The approach of using state-averaged (SA) orbitals is validated through comparisons between different averages and through use of higher order excitations in the WFs for the ionic states. It represents a major extension of our earlier work on the main and satellite features of the Fe 2p XPS of Fe2O3 and proves the reliability and the generality of the assignments of the character and origin of the different features of the XPS obtained with orbitals optimized for SAs. These molecular orbital methods permit the characterization of the ionic states in terms of the importance of shake excitations and of the coupling of ionization of 2p1/2 and 2p3/2 spin-orbit split sub shells. The work lays the foundation for definitive assignments of the character of main and satellite XPS features and points to their origin in the electronic structure of the material.

(Digital Presentation) Study of the Intervalence Charge Transfer in a 18NaCl+Na3SmF6 Model System By Quantum Chemical Methods

The frontier orbital method showed a high informativity for the study of electron transfer in the model system 18NaCl+Na3SmF6. Structures having a high probability of electron transfer from the cathode to the samarium complex were observed when varying the transition state parameters. The influence of the full-symmetric oscillations Sm-F bonds and the boundary ion shift on the activation barrier, the frontier molecular orbitals energy and the delocalization character of the lowest unoccupied molecular orbital wave function in the samarium-containing model systems was systematically studied. This analysis allowed to identify the most probable structures of the transition state for the electron transfer process. The application of the method of frontier orbitals made it possible to determine the structure of the transition state of the complex SmF6 3- near the electrode surface with a small costs of machine time, using an agreement of the calculated and experimental values for the activation energy of electron transfer.

Bardeen's tunneling theory applied to intraorbital and interorbital hopping integrals between dopants in silicon

We utilize Bardeen's tunneling theory to calculate intra- and interorbital hopping integrals between phosphorus donors in silicon using known orbital wave functions. While the two-donor problem can be solved directly, the knowledge of hoppings for various pairs of orbitals is essential for constructing multi-orbital Hubbard models for chains and arrays of donors. To assure applicability to long-range potentials, we rederive Bardeen's formula for the matrix element without assuming non-overlapping potentials. Moreover, we find a correction to the original expression allowing us to use it at short distances. We also show that accurate calculation of the lowest donor-pair eigenstates is possible based on these tunnel couplings, and we characterize the obtained states. The results are in satisfactory quantitative agreement with those obtained with the standard H\"uckel tight-binding method. The calculation relies solely on the wave functions in the barrier region and does not explicitly involve donor or lattice potentials, which has practical advantages. We find that neglecting the central correction potential in the standard method may lead to qualitatively incorrect results, while its explicit inclusion raises severe numerical problems, as it is contained in a tiny volume. In contrast, using wave functions obtained with this correction in the proposed method does not raise such issues. Nominally, the computational cost of the method is to calculate a double integral along the plane that separates donors. For donor separation in directions where valley interference leads to oscillatory behavior, additional averaging over the position of the integration plane is needed. Despite this, the presented approach offers a competitive computational cost as compared to the standard one. This work may be regarded as a benchmark of a promising method for calculating hopping integrals in lattice models.

Optical and magnetic control of orbital flat bands in a polariton Lieb lattice

We study the magneto-optical response of exciton polaritons in $p$-orbital flat bands in a two-dimensional Lieb lattice of semiconductor microcavity pillars. At low excitation density, we detail the influence of an external magnetic field on the exciton component, which enables magnetic tuning of the flat-band states. In the high-density regime, one can induce a spin population imbalance by circularly polarized pumping leading to an effective nonlinear Zeeman splitting. We show how the interplay between the symmetry of the orbital wave function, photonic spin-orbit coupling, and real and effective Zeeman splittings gives rise to real-space flat-band patterns with tilted orbital wave functions in the regime of dynamical polariton condensation. These results demonstrate the ability to optically and magnetically manipulate the spatial, spectral, and polarization properties of polariton condensates in the flat energy bands of a Lieb lattice.

3C-SiC-induced peak emission intensity in photoluminescence spectrum of SiC/SiO2 core–shell nanowires using first-principles calculations

In light of the recent publication of a report on the preparation of crystalline silicon carbide nanowires (NWs) covered with silicon oxide (SiC/SiO2) core–shell nanowires at low temperature, this study uses first-principles calculations based on the related transmission electron microscope micrographs to study hydrogen-passivated 3C-, 2H-, 4H-, and 6H-SiC NWs and their combinations. The aim is to examine charge transfers at the 2H/3C and the 2H/4H/3C interfaces in case there is no limit to periodicity. The orbital wavefunctions in the calculated interfaces exhibited changes from valence band maximum to conduction band minimum. The results of the photoluminescence spectrum showed a peak at a wavelength of 392 nm in terms of the intensity of emission, where this has been expected for such microstructures. Zhang et al. claimed that the source of this peak lies in nanoscale 6H-SiC layers, but our simulations based on experimental measurements indicate that it likely originates in 3C-SiC nanowires with a diameter of 1.5 nm.

Spin-Coupled Generalized Valence Bond Theory: New Perspectives on the Electronic Structure of Molecules and Chemical Bonds

Spin-Coupled Generalized Valence Bond (SCGVB) theory provides the foundation for a comprehensive theory of the electronic structure of molecules. SCGVB theory offers a compelling orbital description of the electronic structure of molecules as well as an efficient and effective zero-order wave function for calculations striving for quantitative predictions of molecular structures, energetics, and other properties. The orbitals in the SCGVB wave function are usually semilocalized, and for most molecules, they can be interpreted using concepts familiar to all chemists (hybrid orbitals, localized bond pairs, lone pairs, etc.). SCGVB theory also provides new perspectives on the nature of the bonds in molecules such as C2, Be2 and SF4/SF6. SCGVB theory contributes unparalleled insights into the underlying cause of the first-row anomaly in inorganic chemistry as well as the electronic structure of organic molecules and the electronic mechanisms of organic reactions. The SCGVB wave function accounts for nondynamical correlation effects and, thus, corrects the most serious deficiency in molecular orbital (RHF) wave functions. Dynamical correlation effects, which are critical for quantitative predictions, can be taken into account using the SCGVB wave function as the zero-order wave function for multireference configuration interaction or coupled cluster calculations.

Evaluation of the Electronic Structure Resulting from ab-initio Calculations on Simple Molecules Using the Molecular Orbital Theory

Hartree Fock (HF) and Density Functional Theory (DFT) have been commonly used to model chemical problems. This study uses the Molecular Orbital Theory (MOT) to evaluate the electronic structure of five diatomic molecules generated by HF and DFT calculations. The evaluation provides an explanation of how the orbitals of a molecule come to be and how this affects the calculation of the physical quantities of the molecule. The evaluation is obtained after comparing the orbital wave functions calculated by MOT, HF, and DFT. This study found that the nature of the Highest Occupied Molecular Orbital (HOMO) of a molecule is determined by the valence orbital properties of the constituent atoms. This HOMO property greatly influences the precision of calculating the molecular electric dipole moment. This shows the importance of understanding the orbital properties of a molecule formed from the HF and DFT calculations

A deep neural network for molecular wave functions in quasi-atomic minimal basis representation.

The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts to answer this question have, among other methods, given rise to semi-empirical quantum chemistry in minimal basis representation. We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [K. T. Schütt et al., Nat. Commun. 10, 5024 (2019)] for electronic wave functions in an optimized quasi-atomic minimal basis representation. For five organic molecules ranging from 5 to 13 heavy atoms, the model accurately predicts molecular orbital energies and wave functions and provides access to derived properties for chemical bonding analysis. Particularly for larger molecules, the model outperforms the original atomic-orbital-based SchNOrb method in terms of accuracy and scaling. We conclude by discussing the future potential of this approach in quantum chemical workflows.

Nanoscale Properties of the Methylation in GpC Dinucleotide Systems

AbstractThe incorporation of a methyl group to DNA nucleotides (methylation) is a well known phenomenon in epigenetic regulation. Methylation can result in gene silencing. Here we investigate the electronic properties of cytosine methylation in different DNA systems using first‐principles density functional theory calculations. Specifically, four systems are investigated consisting of two stacked base pairs, including the deoxyribose‐phosphate backbone. These four systems are the unmethylated GpC‐CpG, the single methylated GpC‐mCpG, the double symmetrical methylated GpCm‐mCpG, and the quadruple symmetrical GpCmm‐mmCpG. Single base‐pair cases are also considered with and without the deoxyribose‐phosphate backbone (with: pG‐pC, pG‐pCm, and pG‐pCmm; without: G−C, G−Cm, and G‐Cmm). These structures are relaxed using the conjugate gradient method. Nanoscale properties, such as the electronic density of states, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) wave functions, charge Mulliken population, hydrogen bond energy, binding energy, and dipole moments between unmethylated and methylated relaxed structures are obtained and compared. These results demonstrate that the deoxyribose‐phosphate backbone plays a crucial role in the spatial distribution of HOMO and LUMO wave functions in the stacked systems modulating reactivity and stability. Cytosine methylation on the GpC‐CpG system results in a stabilization effect. Dipole moment modification in the studied systems could favor specific protein‐DNA interactions due to the methyl group non‐polarity, producing hydrophobic DNA regions. These findings suggest specific rules of interaction between methylated regions and gene silencing elements at the nanoscale level.