Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.     

Complex Geometry and Dirac Equation

Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit . We discuss two possibilities which appearin the multivector algebra approach: the₁₂₃ and ₂₁ complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit is also discussed.     

Tunable diode lasers and two-tone frequency modulation spectroscopy applied to atmospheric gas analysis

In this paper, we discuss the main features of a class of gas analyzers based on spectroscopic techniques with the aim of realizing fully automated systems which can be used for practical purposes. The technique we deal with is based on semiconductor diode laser as sources, emitting in the near infrared region of the electromagnetic spectrum, and the two-tone frequency modulation spectroscopy as the detection technique. We will describe the main features of a typical device and two particular apparata for industrial and biological applications.     

Re-investigation of the166Yb→166Tm Decay

The decay of¹⁶⁶Yb has been investigated with high-resolution Ge(Li) detectors. The intensity of any γ ray other than that at 82.29 keV is less than 0.3% per decay. The total decay energy was redetermined asQ=215 _?18 ⁺³³ keV. An upper limitF _w< 150 was determined for the hindrance factor of theF-forbidden 82.29 keV transition.     

Reactions of 14N and 16O ions with light nuclei at Elab = 16–58 MeV

Yield curves for formation of ⁷Be and other radio-nuclides from bombardment of C, Al and Si targets with 16–58 MeV ¹⁴N and ¹⁶O ions were measured. The ⁷Be yields disagree by several orders of magnitude with Hauser-Feshbach and transition-state predictions. The other yields are in order-of-magnitude agreement with nucleon and/or α-particle evapolation calculations.     

Oxygen adsorption on Cu(110): Determination of atom positions with low energy ion scattering

The position of adsorbed oxygen on Cu($\text{1}$10) surfaces was determined with Low Energy Ion Scattering (LEIS). The experiments were performed by bombarding the copper surface at small angles of incidence with low energy Ne⁺ ions (3–5 keV). Measurements of the Ne⁺ ions scattered by adsorbed oxygen showed regular peaks in the azimuthal distribution of the scattered ions due to a shadowing effect. From the symmetry of the azimuthal distributions it follows that the centre of an adsorbed oxygen atom on the Cu(1&#x0304;10) surface lies about 0.6 Å below the midpoint between two neighbouring Cu atoms in a 〈001〉 row. A comparison of the azimuthal distributions of Ne⁺ ions scattered from clean Cu surfaces and oxygen-covered Cu surfaces showed that hardly any surface reconstruction had occurred in the oxygen-covered surfaces. The applied method seems to be an appropriate one for locating adsorbed atoms because it uses only simple qualitative considerations about azimuthal distributions of scattered ions.     

The use of Raman microscopy and laser desorption ionization mass spectrometry in the examination of synthetic organic pigments in modern works of art

Synthetic organic pigments are widely used in modern and contemporary works of art. They have been examined by a variety of techniques including spectroscopic methods such as Fourier transform infrared spectroscopy, Raman, and X‐ray powder diffraction as well as chromatographic or mass spectrometric techniques such as pyrolysis‐gas chromatography/mass spectrometry and laser desorption ionization mass spectrometry (LDI–MS). Often, a combination of techniques has been used to examine these pigments. This paper describes use of Raman spectroscopy to create a database of colorants including two pigments not previously reported, PO1 and PO2. Then, using Raman spectroscopy in combination with LDI–MS, samples from modern works of art by artists including Mark Rothko, Barnett Newman, and José de Rivera were examined in order to identify the pigments present. One finding was that Rothko used a variety of red pigments over the course of his career including PR11 which has not been previously reported in artwork, and PO2 found with its positional isomer PR1. Knowledge of the colorants serves to inform conservators about display and treatment decisions. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

C imaging by double resonance scalar-coupling editing

The two-dimensional FT Imaging of ¹³C-glucose obtained with twin spin-echo double resonance sequence is presented. The images have been obtained by a doubly tuned surface coil on samples containing water and ¹³C-enriched glucose in water. It is shown, both theoretically and experimentally, that the whole editing capability of the twin spin-echo double resonance imaging sequence is also preserved in the presence of the radiofrequency field inhomogeneity produced by the surface coil. As in an efficient selective irradiation method, the enhancement in the signal-to-noise ratio with respect to the direct ¹³C detection, depends on the number of protons J-coupled to ¹³C.     

Highly excited “nuclear molecules”: A way to explain the fluctuations in DBHIC excitation functions. Study of the28Si +28Si colliding system at 5.3 MeV ·A

The properties of the strong fluctuations observed in the excitation functions of Dissipative Binary Heavy Ion Collisions (DBHIC) have been studied for the system²⁸Si+²⁸Si in the energy range 150 MeV ≤E _lab ≤ 156 MeV with 150 keV step laboratory incident energy, by angular distributions and excitation functions measurements. Experimental results are compared to the the recently developed Partially Overlapping Molecular Level Model (POMLM). The parameters of the model have been determined with reasonable accuracy by describing all the quantities characterizing the fluctuations in the excitation functions i.e.: Average Angular Distributions, Energy Autocorrelation Functions, Variances, Angular Correlation Coefficients. The results of the analysis strongly support the idea of a process proceeding through the formation of an highly excited “nuclear molecule”. Experimental data collected at the most forward angles show the effects of strong excitation of a few final channels.