Orbital Description Research Articles

Electronic couplings for singlet oxygen photosensitization and its molecular orbital overlap description

The reaction of triplet fusion, also named triplet-triplet annihilation, has attracted a lot of research interests because of its wide applications in photocatalytic, solar cells, and bioimaging. As for the singlet oxygen photosensitization, the reactive singlet oxygen species are generated through the energy transfers from photosensitizer (PS) to ground triplet oxygen molecule. In this work, we computed the electronic coupling for singlet oxygen photosensitization using the nonadiabatic coupling from the quantum chemical calculation. Then we utilized the molecular orbital (MO) overlaps to approximate it, where the MOs were computed from isolated single molecules. As demonstrated with quantitative results, this approach well describes the distribution of the coupling strength as the function of the intermolecular distance between the sensitizer and O2, providing us a simple but effective way to predict the coupling of triplet fusion reactions.

ECD exciton chirality method today: a modern tool for determining absolute configurations.

The application of the exciton chirality method (ECM) to interpret electronic circular dichroism (ECD) spectra is a well‐established and still popular approach to assign the absolute configuration (AC) of natural products, chiral organic compounds, and organometallic species. The method applies to compounds containing at least two chromophores with electric dipole allowed transitions (e.g., π–π* transitions). The exciton chirality rule correlates the sign of an exciton couplet (two ECD bands with opposite sign and similar intensity) with the overall molecular stereochemistry, including the AC. A correct application of the ECM requires three main prerequisites: (a) the knowledge of the molecular conformation, (b) the knowledge of the directions of the electric transition moments (TDMs), and (c) the assumption that the exciton coupling mechanism must be the major source of the observed ECD signals. All these prerequisites can be easily verified by means of quantum‐mechanical (QM) calculations. In the present review, we shortly introduce the general principles that underpin the use of the ECM for configurational assignments and survey its applications, both classic ones and some reported in the recent literature. Based on these examples, we will stress the advantages of the ECM but also the key requisites for its correct application. Additionally, we will discuss the dependence of the couplet sign on geometrical parameters (angles α,β,γ between TDMs), which can be helpful for discerning the sign of exciton chirality in ambiguous situations. Finally, we will present a molecular orbital (MO) description of the exciton coupling phenomenon.

Extended first-principles molecular dynamics model for high temperature simulations in the Abinit code: Application to warm dense aluminum

The extended first-principles molecular dynamics (Extended FPMD) model introduced by Zhang et al. [2], based on an analytical single plane wave description of electronic orbitals for high energy electrons, has been implemented within the ab initio DFT software package Abinit and is now available. This model allows quantum simulations to be done smoothly on the full range of temperatures from cold condensed matter to hot dense plasmas passing through the warm dense matter regime which was currently not possible within the same ab initio model due to numerical limitations. In addition to presenting a brief theoretical background of the Zhang et al. method, we propose some improvements to the model. We then present the details of the implementation, and finally offer an application to the aluminum simulations for multiple densities, from room temperature to hot (thousands of eVs) temperature ranges, with a resulting Hugoniot equation of state that we compare with other methods.

A unified molecular‐wide and electron density based concept of chemical bonding

AbstractChemical bonding is at heart but, not being a quantum mechanical‐defined physical property of a system, is a subject of endless and often fruitless debates. Having so many and very different models of chemical bonding without knowing what this really is does not make it easier. There is, however, a general agreement that concentrating electron density (ED) in and delocalizing ED to internuclear region is always associated with minimizing system's energy and synonymous with chemical bonding. Fragment, atomic, localized, delocalized, and interatomic (FALDI)‐based density analysis involves entire space occupied by a molecule. From this molecular‐wide and density‐based methodology, it is possible to quantify localized and delocalized by all atoms ED at any coordinater, including critical points on Bader's molecular graphs. Each atom and atom‐pair contributions of delocalized density are quantified to reveal major players in the all‐atom and molecular‐wide chemical bonding. Partitioning the total ED to individual molecular or natural orbital's contributions using MO‐ED and MO‐DI methods, in conjunction with one dimensional (1D) cross section methodology, generates an orbital‐based molecular‐wide picture. This provides, besides reproducing results from FALDI, qualitative description of orbitals' nature that correlates well with classical understanding of bonding, nonbonding, and antibonding orbitals. A qualitative and quantitative impact of an immediate, distant, or molecular‐wide molecular environment on intra‐ and intermolecular di‐atomic, intra‐ and interfragment interactions is the domain of the Fragment Attributed Molecular System Energy Change (FAMSEC) family of methods. The FALDI, FAMSEC, MO‐ED, MO‐DI, and 1D cross section methodologies provide consistent and quantifiable physics‐based picture of molecular‐wide chemical bonding without invoking unicorns, such as a chemical bond.This article is categorized under:Electronic Structure Theory > Density Functional TheoryElectronic Structure Theory > Ab Initio Electronic Structure MethodsMolecular and Statistical Mechanics > Molecular Interactions

On the Semisimple Orbits of Restricted Cartan Type Lie Algebras W, S and H

In this short note, we give a description of semisimple orbits in the restricted Cartan type Lie algebras W, S, H.

Density-Matrix Based Scheme of Basis Selection for Linear Combination of Fragment Molecular Orbitals

A dependable description of the frontier orbitals around the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is essential for the theoretical elucidatio...

Ultrafast Transfer and Transient Entrapment of Photoexcited Mg Electron in Mg@C_{60}.

Electron relaxation is studied in endofullerene Mg@C_{60} after an initial localized photoexcitation in Mg by nonadiabatic molecular dynamics simulations. Two approaches to the electronic structure of the excited electronic states are used: (i)an independent particle approximation based on a density-functional theory description of molecular orbitals and (ii)a configuration-interaction description of the many-body effects. Both methods exhibit similar relaxation times, leading to an ultrafast decay and charge transfer from Mg to C_{60} within tens of femtoseconds. Method (i)further elicits a transient trap of the transferred electron that can delay the electron-hole recombination. Results shall motivate experiments to probe these ultrafast processes by two-photon transient absorption or photoelectron spectroscopy in gas phase, in solution, or as thin films.

An orbital construction of optimum distance flag codes

Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space Fqn, where q is a prime power and Fq, the finite field of size q. In this paper we study the construction on Fq2k of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension k and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on Fq2k having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on Fq2k that strongly depends on the characteristic of the field.

Approximate analytic solution of nonlinear Riccati spacecraft formation flying dynamics in terms of orbit element differences

Generally, spacecraft relative orbit is described using Hill frame coordinates with which it is difficult to obtain precise orbit geometry. The orbit description is made simpler and spacecraft relative trajectory easier to track using relative orbit element differences with the chief spacecraft true latitude (θ) and the difference between deputy and chief spacecraft true latitude (δθ) being the only time-varying parameters. Via the approach of parameterized orbit element differences and transformation, this paper develops approximate analytic solutions of nonlinear Riccati spacecraft formation flying relative motion dynamics. The algorithm for the computations of the δθ solutions is developed and it is based on well-structured and defined step-by-step instructions. As shown by the numerical simulations, the Riccati model gave a better approximation with lesser error making it amenable for the spacecraft formation flying, rendezvous analysis, spacecraft guidance, navigation and control.

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.

Index of multi-determinantal and multi-reference character in coupled-cluster theory.

A full configuration interaction calculation (FCI) ultimately defines the innate molecular orbital description of a molecule. Its density matrix and the natural orbitals obtained from it quantify the difference between having N-dominantly occupied orbitals in a reference determinant for a wavefunction to describe N-correlated electrons and how many of those N-electrons are left to the remaining virtual orbitals. The latter provides a measure of the multi-determinantal character (MDC) required to be in a wavefunction. MDC is further split into a weak correlation part and a part that indicates stronger correlation often called multi-reference character (MRC). If several virtual orbitals have high occupation numbers, then one might argue that these additional orbitals should be allowed to have a larger role in the calculation, as in MR methods, such as MCSCF, MR-CI, or MR-coupled-cluster (MR-CC), to provide adequate approximations toward the FCI. However, there are problems with any of these MR methods that complicate the calculations compared to the uniformity and ease of application of single-reference CC calculations (SR-CC) and their operationally single-reference equation-of-motion (EOM-CC) extensions. As SR-CC theory is used in most of today's "predictive" calculations, an assessment of the accuracy of SR-CC at some truncation of the cluster operator would help to quantify how large an issue MRC actually is in a calculation, and how it might be alleviated while retaining the convenient SR computational character of CC/EOM-CC. This paper defines indices that identify MRC situations and help assess how reliable a given calculation is.

Closed form parametric solutions of nonlinear Abel-type and Riccati-type spacecraft relative motion

In comparison to the conventional approach of using Cartesian coordinates to describe spacecraft relative motion, the relative orbit description using Keplerian orbital elements provides a better visualization of the relative motion due to the benefit of having only one term (anomaly) that changes with time out of the six orbital elements leading to the reduction of the number of terms to be tracked from six, as in the case of Hill coordinates, to one. In this paper, under certain assumptions and transformations, the spacecraft relative equations of motion, in terms of orbital element differences, is approximated into the nonlinear first kind Abel-type and Riccati-type differential equations. Furthermore, we present methodologies for the formulation of the close form analytical solutions of the approximated equations. As shown by the numerical simulations, the closed form solutions and the nonlinear equations are in conformity with Riccati-type equations having higher errors than the Abel-type equations. This shows that the Abel-type equation, a third order polynomial, approximated the relative motion better than the Riccati-type equation, a second order polynomial. The resulting new analytical solutions gave better insight into the relative motion dynamics and can be used for the analysis of spacecraft formation flying, proximity and rendezvous operations.

Casimir Functions of Free Nilpotent Lie Groups of Steps 3 and 4

Any free nilpotent Lie algebra is determined by its rank and step. We consider free nilpotent Lie algebras of steps 3, 4 and corresponding connected and simply connected Lie groups. We construct Casimir functions of such groups, i.e., invariants of the coadjoint representation. For free 3-step nilpotent Lie groups we get a full description of coadjoint orbits. It turns out that general coadjoint orbits are affine subspaces, and special coadjoint orbits are affine subspaces or direct products of nonsingular quadrics. The knowledge of Casimir functions is useful for investigation of integration properties of dynamical systems and optimal control problems on Carnot groups. In particular, for some wide class of time-optimal problems on 3-step free Carnot groups we conclude that extremal controls corresponding to two-dimensional coadjoint orbits have the same behavior as in time-optimal problems on the Heisenberg group or on the Engel group.

A version of Calderón–Mityagin theorem for the class of rearrangement invariant groups

Let l0 be the group (with respect to the coordinate-wise addition) of all sequences of real numbers x=(xk)k=1∞ that are eventually zero, equipped with the quasi-norm ‖x‖0=card{suppx}. A description of orbits of elements in the pair (l0,l1) is given, which complements (in the sequence space setting) the classical Calderón–Mityagin theorem on a description of orbits of elements in the pair (l1,l∞). As a consequence, we obtain that the pair (l0,l1) is K-monotone.

Analysis of Cassini radio tracking data for the construction of INPOP19a: A new estimate of the Kuiper belt mass

Context. Recent discoveries of new trans-Neptunian objects have greatly increased the attention by the scientific community to this relatively unknown region of the solar system. The current level of precision achieved in the description of planet orbits has transformed modern ephemerides in the most updated tools for studying the gravitational interactions between solar system bodies. In this context, the orbit of Saturn plays a primary role, especially thanks to Cassini tracking data collected during its 13-year mission around the ringed planet. Planetary ephemerides are currently mainly built using radio data, in particular with normal points derived from range and Doppler observables exchanged between ground stations and interplanetary probes. Aims. We present an analysis of Cassini navigation data aimed at producing new normal points based on the most updated knowledge of the Saturnian system developed throughout the whole mission. We provide additional points from radio science dedicated passes of Grand Finale orbits and Titan flybys. An updated version of the INPOP planetary ephemerides based upon these normal points is presented, along with a new estimate of the mass of trans-Neptunian object rings located in the 2:1 and 3:2 mean motion resonances with Neptune. Methods. We describe in detail the orbit determination process performed to construct the normal points and their associated uncertainties and how we process those points to produce a new planetary ephemeris. Results. From the analysis, we obtained 623 new normal points for Saturn with metre-level accuracy. The ephemeris INPOP19a, including this new dataset, provides an estimated mass for the trans-Neptunian object rings of (0.061 ± 0.001)M⊕.

Electronic Structural Studies of the Ru3(III,II,II) Mixed-Valent State of Oxo-Centered Triruthenium Clusters

The anionic state of basic ruthenium acetate complexes of the type [Ru3O(OAc)6](CO)(L1)(L2) (L = 4-cyanopyridine, pyridine, and N,N-dimethylaminopyridine) feature pronounced optical transitions in the near-infrared region indicative of strongly coupled mixed-valence states. A series of these clusters was prepared and studied spectroscopically in tandem with density functional theory (DFT) computational results to construct an orbital structure-function description of how the electron density is shared between the ruthenium centers in this mixed-valent state. The mixed-valency manifests itself as a combination of the nonbonding atomic orbitals of the equivalent ruthenium centers, with increased energetic splitting between the orbitals with symmetries appropriate for more efficient electronic communication. This DFT-based model agrees with the Marcus-Hush description of mixed-valency, with the added knowledge that specific orbitals contribute to different degrees in the electronic coupling between two redox centers.

Description of infinite orbits on multiple projective spaces

Let G be the general linear group of the degree n≥2 over an algebraically closed field K. In this article, we describe the orbit decomposition of a product of copies of Pn−1K under the diagonal action of G. We also construct representatives of orbits. If m≥4, the number of orbits is infinite, and we give a description of them.

Orbitals Permit the Interpretation of Core-Level Spectroscopies in Terms of Chemistry

We present evidence that the use of orbital based analyses provides an important fundamental basis for interpreting and understanding the significance of features in core-level spectroscopies, in particular, X-ray photoelectron spectroscopy, XPS. A recent paper by Truhlar and colleagues cautions about the limitations of orbital based interpretations of photoelectron spectroscopy for the accurate modeling of the electronic structure of the ions. We provide an alternate view that does use orbitals to derive detailed information from XPS. We discuss the appropriate meaning of Koopmans’ theorem as a way to separate the chemically interesting initial state contributions to XPS binding energies, BEs, from the less interesting properties of highly excited ionic states, rather than as a way to estimate values of BEs and BE shifts. The use of orbitals and orbital occupations to take into account the spin and orbital angular momentum coupling that leads to the observed XPS multiplets is shown to be important to understand the number and energy spread of XPS features. The use of a standard approximation to determine the XPS intensities, essential for the theoretical prediction of XPS spectra, is shown to depend on the concept of ionization of electrons from specific orbitals. Finally, the use of orbital properties to identify and include the main many electron correlation of the ionic states in XPS is described. The importance of these considerations is shown by describing examples where they are used in the theoretical determination and the theoretical analysis of the XPS of representative systems. The orbital description of XPS is shown schematically below for the Ne atom. An orbital description can be applied to and is appropriate to understand the photoemission of complex systems.

Loose ends in a strong force 3-body problem

Up to symmetries, the orbits of three equal masses under an inverse cube force with zero angular momentum and constant moment of inertia can be reparametrized as the geodesics of a complete, negatively curved metric on a pair of pants. The ends of the pants represent binary collisions. Here we will examine the visibility properties of such negatively curved surfaces, allowing a description of orbits beginning or ending in binary collisions of this 3-body problem.

Following the evolution of excited states along photochemical reaction pathways.

Analyzing the behavior of potential energy surfaces (PESs) of diabatic excited states (ESs) becomes of crucial importance for a complete understanding of complex photochemical reactions. Since the definition of a compact representation for the transition density matrix, the use of the natural transition orbitals (NTOs) has become a routine practice in time-dependent density functional theory calculations. Their popularity has remarkably grown due to its simple orbital description of electronic excitations. Indeed, very recently, we have presented a new formalism used for the optimization of ESs by tracking the state of interest computing the NTO's overlap between consecutive steps of the procedure. In this new contribution, we generalize the use of this NTO's overlap-based state-tracking formalism for the analysis of all the desired diabatic states along any chemical reaction pathway. Determining the PES of the different diabatic states has been automatized by developing an extension of our recently presented algorithm, the so-called SDNTO: "Steepest Descent minimization using NTOs." This automatized overlap-based procedure allows an agile and convenient analysis of the evolution of the ESs avoiding the intrinsic ambiguity of visualizing orbitals or comparing physical observables. The analysis of two photochemical reactions of the same nature with different PES landscapes perfectly illustrates the utility of this new tool.