Orbital Sets Research Articles

THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

Chemical bonding theories as guides for self-interaction corrected solutions: Multiple local minima and symmetry breaking.

Fermi-Löwdin orbitals (FLOs) are a special set of localized orbitals, which have become commonly used in combination with the Perdew-Zunger self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained for a set of occupied orbitals by specifying a classical position for each electron. These positions are known as Fermi-orbital descriptors (FODs), and they have a clear relation to chemical bonding. In this study, we show how FLOs and FODs can be used to initialize, interpret, and justify SIC solutions in a common chemical picture, both within FLO-SIC and in traditional variational SIC, and to locate distinct local minima in either of these approaches. We demonstrate that FLOs based on Lewis theory lead to symmetry breaking for benzene-the electron density is found to break symmetry already at the symmetric molecular structure-while ones from Linnett's double-quartet theory reproduce symmetric electron densities and molecular geometries. Introducing a benchmark set of 16 planar cyclic molecules, we show that using Lewis theory as the starting pointcan lead to artifactual dipole moments of up to 1D, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking. The role of hovering FODs is also briefly discussed.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method.

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

Fluoromaticity: The Molecular Orbital Contributions of Fluorine Substituents to the π-Systems of Aromatic Rings.

The addition of fluorine atoms to an aromatic ring brings about an additional set of π-bonding and antibonding orbitals culminating after the addition of the sixth fluorine with a new set of π-aromatic-like orbitals that affect the molecule in a way that we will refer to hereafter as “fluoromaticity”. Depending on the number and position of the fluorine atoms, the contributed π-orbitals can even further stabilize the ring leading to smaller bond lengths within the ring and higher resistance to addition reactions. This added ring stability partially explains the high thermostability and chemical resistance found in polymers containing fluorinated aromatics in their architecture. A similar molecular orbital effect is seen with the addition of other halogen atoms to aromatic rings, though to a much smaller degree and not resulting in the additional ring stability.

Quantum chemical studies on structural, spectroscopic, nonlinear optical, and thermodynamic properties of the 1,2,4-triazole compound

AbstractIn this study, the structure of 4-[4-(diethylamino)-benzylideneamino]-5-benzyl-2H-1,2,4-triazol-3(4H)-one (DBT) was examined through spectroscopic and theoretical analyses. In this respect, the geometrical, vibrational frequency,1H and13C-nuclear magnetic resonance (NMR) chemical shifts, thermodynamic, hyperpolarizability, and electronic properties including the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energies of DBT as a potential non-linear optical (NLO) material were investigated using density functional theory at the B3LYP level with the 6-311G basis set.1H and13C-NMR chemical shifts of DBT with the gauge-invariant atomic orbital and continuous set of gauge transformation methods (in the solvents) were estimated, and the computed chemical shift values displayed excellent alignment with observed ones. Time-dependent density-functional theory (TD-DFT) calculations with the integral equation formalism polarizable continuum model within various solvents and gas phases in the ground state were used to evaluate UV-vis absorption and fluorescence emission wavelengths. Thermodynamic parameters including enthalpy, heat capacity, and entropy for DBT were also calculated at various temperatures. Moreover, calculations of the NLO were carried out to obtain the title compound’s electric dipole moment and polarizability properties. To illustrate the effect of the theoretical method on the spectroscopic and structural properties of DBT, experimental data of structural and spectroscopic parameters were used. The correlational analysis results were observed to indicate a strong relationship between the experimental and theoretical results.

A complex Gaussian approach to molecular photoionization.

We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by nonlinear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH3 and H2 O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.

Photoionisation of the CH radical using the B-spline R-matrix method

Aims. The primary motivation for this paper is to provide accurate data for the photoionisation of the CH radical, including the absolute total photoionisation cross-section, partial cross-sections, and photoelectron angular distribution. In addition, the near threshold features in the photoionisation curve (which are absent in previous studies) are produced with high precision. Methods. A multichannel wavefunction based on the R-matrix approach, which uses the configuration interaction (CI) method to describe electronic correlation, is carried out in the present calculations. A set of B-spline orbitals is employed to represent the accurate continuum. The distinctive feature of the present calculations allows us to generate a more accurate description of the bound and continuum states than those employed before. Results. Total photoionisation cross-sections from the ground state of CH radicals and partial cross-sections corresponding to 1π, 3σ, and 2σ states of CH+ ions are presented for photon energies ranging from threshold to 80 eV. Extensive resonance structures, which are absent in previous studies, are observed for the first time near the ionisation threshold. The cross-section dataset obtained from the present calculations is expected to be sufficiently accurate and comprehensive for most current modelling applications involving the photon and CH radical scattering system.

Multi-reference approach to the computation of double core-hole spectra.

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K-2) are obtained for H2O, N2, CO, and C2H2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K-2 shake-up spectra of H2O and C2H2n molecules are here completely characterized for the first time.

Spin-resolved charge density and wavefunction refinements using MOLLYNX: a review

MOLLYNX is a new crystallographic tool developed to access a more precise description of the spin-dependent electron density of magnetic crystals, taking advantage of the richness of experimental information from high-resolution X-ray diffraction (XRD), unpolarized neutron (UND) and polarized neutron diffraction (PND). This new program is based either on the well known Hansen–Coppens multipolar model (MOLLYNX-mult) or on a new expansion over a set of atomic orbitals (MOLLYNX-orb). The main difference between the two models is the basis of the expansion: in MOLLYNX-mult the expansion is over atom centered real spherical harmonics, in MOLLYNX-orb the expansion is over a set of atomic orbitals with which mono and bicentric contributions are calculated. This new approach of MOLLYNX-orb can also be applied to nonmagnetic crystals. This paper summarizes the theoretical ground of two models and describes the first applications to organic, organometallic and inorganic magnetic materials

Potential Energy Curves of Molecular Nitrogen for Singly and Doubly Ionized States with Core and Valence Holes.

Theoretical description of potential energy curves (PECs) of molecular ions is essential for interpretation and prediction of coupled electron-nuclear dynamics following ionization of parent molecule. However, an accurate representation of these PECs for core or inner valence ionized state is nontrivial, especially at stretched geometries for double- or triple-bonded systems. In this work, we report PECs of singly and doubly ionized states of molecular nitrogen using state-of-the-art quantum chemical methods. The valence, inner valence, and core ionized states have been computed. A double-loop optimization scheme that separates the treatment of the core and the valence orbitals during the orbital optimization step of the multiconfiguration self-consistent field method has been implemented. This technique allows the energy to be converged to any desired ionized state with any number of core or inner-shell holes. The present work also compares the PECs obtained using both delocalized and localized sets of orbitals for the core hole states. The PECs of a number of singly and doubly ionized valence states have also been computed and compared with previous studies. The computed PECs reported here are expected to be of importance for future studies to understand the interplay between photoionization and Auger spectra during the breakup of molecular nitrogen when interacting with intense free electron lasers.

Reeb orbits that force topological entropy

Abstract We develop a forcing theory of topological entropy for Reeb flows in dimension three. A transverse link L in a closed contact $3$ -manifold $(Y,\xi )$ is said to force topological entropy if $(Y,\xi )$ admits a Reeb flow with vanishing topological entropy, and every Reeb flow on $(Y,\xi )$ realizing L as a set of periodic Reeb orbits has positive topological entropy. Our main results establish topological conditions on a transverse link L, which imply that L forces topological entropy. These conditions are formulated in terms of two Floer theoretical invariants: the cylindrical contact homology on the complement of transverse links introduced by Momin [A. Momin. J. Mod. Dyn.5 (2011), 409–472], and the strip Legendrian contact homology on the complement of transverse links, introduced by Alves [M. R. R. Alves. PhD Thesis, Université Libre de Bruxelles, 2014] and further developed here. We then use these results to show that on every closed contact $3$ -manifold that admits a Reeb flow with vanishing topological entropy, there exist transverse knots that force topological entropy.

Advanced modeling of materials with PAOFLOW 2.0: New features and software design

Recent research in materials science opens exciting perspectives to design novel quantum materials and devices, but it calls for quantitative predictions of properties which are not accessible in standard first principles packages. PAOFLOW, is a software tool that constructs tight-binding Hamiltonians from self-consistent electronic wavefunctions by projecting onto a set of atomic orbitals. The electronic structure provides numerous materials properties that otherwise would have to be calculated via phenomenological models. In this paper, we describe recent re-design of the code as well as the new features and improvements in performance. In particular, we have implemented symmetry operations for unfolding equivalent k-points, which drastically reduces the runtime requirements of first principles calculations, and we have provided internal routines of projections onto atomic orbitals enabling generation of real space atomic orbitals. Moreover, we have included models for non-constant relaxation time in electronic transport calculations, doubling the real space dimensions of the Hamiltonian as well as the construction of Hamiltonians directly from analytical models. Importantly, PAOFLOW has been now converted into a Python package, and is streamlined for use directly within other Python codes. The new object oriented design treats PAOFLOW’s computational routines as class methods, providing an API for explicit control of each calculation.

General construction of flat bands with and without band crossings based on wave function singularity

In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS) and also the singularity of the flat-band wave function obtained by a Fourier transform of the CLS (FT-CLS). In order to construct a flat-band model systematically using these ingredients, we first choose a CLS with a specific symmetry representation in a given lattice. Then, the singularity of FT-CLS indicates whether the resulting flat band exhibits a band crossing point or not. A tight-binding Hamiltonian with the flat band corresponding to the FT-CLS is obtained by introducing a set of basis molecular orbitals, which are orthogonal to the FT-CLS. Our construction scheme can be systematically applied to any lattice so that it provides a powerful theoretical framework to study exotic properties of both gapped and gapless flat bands arising from their wave function singularities.

Active orbital preservation for multiconfigurational self-consistent field.

We introduce Active Orbital Preservation for Multiconfigurational Self-Consistent Field (AOP-MCSCF), an automated approach to improving the consistency of active space orbitals over multiple molecular configurations. Our approach is based on maximum overlap with a reference set of active space orbitals taken from a single geometry of a chromophore in the gas phase and can be used to automatically preserve the appropriate orbitals of the chromophore across multiple thermally sampled configurations, even when the chromophore is solvated by quantum-mechanically treated water molecules. In particular, using the singular value decomposition of a Molecular Orbital (MO) overlap matrix between the system and reference, we rotate the MOs of the system to align with the reference active space orbitals and use the resulting rotated orbitals as an initial guess to a MCSCF calculation. We demonstrate the approach on aqueous p-hydroxybenzylidene-imidazolinone (HBI) and find that AOP-MCSCF converges to the "correct" orbitals for over 90% of 3000 thermally sampled configurations. In addition, we compute the linear absorption spectrum and find excellent agreement with new experimental measurements up to 5.4eV (230nm). We show that electrostatic contributions to the solvation energy of HBI largely explain the observed state-dependent solvatochromism.

An Exchange Mechanism for the Magnetic Behavior of Er3+ Complexes.

We study the magnetic properties of the erbium based compounds, Na[Er(WO)] and [(Pc)Er{Pc{N(CH)}}], in the framework of an effective spin exchange model involving delocalized electrons occupying molecular orbitals. The calculations successfully reproduce the experimental data available in the literature for the magnetic spectrum, magnetization and molar susceptibility in dc and ac fields. Owing to their similar molecular geometry, the compounds’ magnetic behaviors are interpreted in terms of the same set of active orbitals and thus the same effective spin coupling scheme. For all three complexes, the model predicts a prompt change in the ground state from a Kramer’s doublet at zero fields to a fully polarized quartet one brought about by the action of an external magnetic field without Zeeman splitting. This alteration is attributed to the enhancement of the effect of orbital interactions over the spin exchange as the magnitude of the external magnetic field increases.

Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem

AbstractWe consider a class of autonomous Hamiltonian systems subject to small, time‐periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation parameter is non‐zero.We describe a topological method to establish orbits which diffuse in energy for every suitably small perturbation parameter . The method yields quantitative estimates: the existence of orbits along which the energy drifts by an amount independent of ε; the time required by such orbits to drift is ; the existence of orbits along which the energy makes chaotic excursions; explicit estimates for the Hausdorff dimension of the set of such chaotic orbits; the existence of orbits along which the time evolution of energy approaches a stopped diffusion process (Brownian motion with drift), as ε tends to 0. For each ε fixed, the set of initial conditions of the orbits that yield the diffusion process has positive Lebesgue measure, and in the limit the measure of these sets approaches 0. Moreover, we can obtain any desired values of the drift and variance for the limiting Brownian motion for appropriate sets of initial conditions. A key feature of our topological method is that it can be implemented in computer‐assisted proofs. We give an application to a concrete model of the planar elliptic restricted three‐body problem, on the motion of an infinitesimal body relative to the Neptune‐Triton system. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

A Globally Averaged Thermospheric Density Data Set Derived From Two‐Line Orbital Element Sets and Special Perturbations State Vectors

AbstractWe describe a long‐term data set of global average thermospheric mass density derived from orbit data on ∼7,700 objects in low Earth orbit, via the effect of atmospheric drag. The data cover the years 1967–2019 and altitudes 250–575 km, and the temporal resolution is 3–4 days for most years. The data set is an extension and revision of a previous version. The most important change is the use of more precise orbit data: special perturbation state vectors are now used starting in 2001, instead of mean Keplerian orbital elements. The data are suitable for climatological studies of thermospheric variations and trends, and for space weather studies on time scales longer than 3 days.

Hyperconvergence in topological dynamics

In this manuscript the concept of hyperspace is revisited. The main purpose is to study hyperconvergence and continuity of orbital and limit set functions for semigroup action on completely regular space. Some general facts on Hausdorff and Kuratowski hyperconvergence are presented.

Integer dynamics

Let [Formula: see text] be an integer, and write the base [Formula: see text] expansion of any non-negative integer [Formula: see text] as [Formula: see text], with [Formula: see text] and [Formula: see text] for [Formula: see text]. Let [Formula: see text] denote an integer polynomial such that [Formula: see text] for all [Formula: see text]. Consider the map [Formula: see text], with [Formula: see text]. It is known that the orbit set [Formula: see text] is finite for all [Formula: see text]. Each orbit contains a finite cycle, and for a given [Formula: see text], the union of such cycles over all orbit sets is finite. Fix now an integer [Formula: see text] and let [Formula: see text]. We show that the set of bases [Formula: see text] which have at least one cycle of length [Formula: see text] always contains an arithmetic progression and thus has positive lower density. We also show that a 1978 conjecture of Hasse and Prichett on the set of bases with exactly two cycles needs to be modified, raising the possibility that this set might not be finite.

Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices.

Due to the presence of non-linear equations, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular solutions was not performed before. In this work, we use two-particle density matrices to investigate local spin and charge correlators that quantify the charge resonance and covalent characters of these solutions. When applied within the unrestricted orbital set, spin correlators elucidate the broken symmetry of the solutions, containing necessary information for building effective magnetic Hamiltonians. Based on GW and GF2 calculations of simple molecules and transition metal complexes, we construct Heisenberg Hamiltonians, four-spin-four-center corrections, and biquadratic spin-spin interactions. These Hamiltonian parameterizations are compared to previous wave-function calculations.