Orbital Scales Research Articles

Charge transfer excitation energies from ground state density functional theory calculations.

Calculating charge transfer (CT) excitation energies with high accuracy and low computational cost is a challenging task. Kohn-Sham density functional theory (KS-DFT), due to its efficiency and accuracy, has achieved great success in describing ground state problems. To extend to excited state problems, our group recently demonstrated an approach with good numerical results to calculate low-lying and Rydberg excitation energies of an N-electron system from a ground state KS or generalized KS calculations of an (N - 1)-electron system via its orbital energies. In the present work, we explore further the same methodology to describe CT excitations. Numerical results from this work show that performance of conventional density functional approximations (DFAs) is not as good for CT excitations as for other excitations due to the delocalization error. Applying localized orbital scaling correction (LOSC) to conventional DFAs, a recently developed method in our group to effectively reduce the delocalization error, can improve the results. Overall, the performance of this methodology is better than time dependent DFT (TDDFT) with conventional DFAs. In addition, it shows that results from LOSC-DFAs in this method reach similar accuracy to other methods, such as ΔSCF, G0W0 with Bethe-Salpeter equations, particle-particle random phase approximation, and even high-level wavefunction methods like CC2. Our analysis shows that the correct 1/R trend for CT excitation can be captured from LOSC-DFA calculations, stressing that the application of DFAs with the minimal delocalization error is essential within this methodology. This work provides an efficient way to calculate CT excitation energies from ground state DFT.

Anisotropic Stark effect of carbon monoxide: emergent orbital cooperativity

ABSTRACT Applying external electric fields to molecules gives rise to spectral shifting and splitting, a phenomenon known as the Stark effect. However, a fundamental question of how electronic structures of molecules are modified by electric fields is still not well understood. By applying electric fields to a carbon monoxide molecule, herein we have successfully addressed the fundamental question at orbital scales and discovered that the Stark effect exhibits anisotropic characters depending on the direction of the electric fields with respect to the molecular axis. Based on the fact that applying electric fields along the molecular axis always preserved the orthogonality between the sigma and pi electrons, we found that orbital resemblance-based cooperativity can only operate within either the sigma system in which sigma electrons somehow prefer to resemble each other or the pi electron system in which the 1π electrons experience polarization-based self-resemblance. However, switching the electric field vertical to the molecular axis breaks down the orthogonality between the sigma system and pi electron systems, opening up electronic channels that allow σ electron systems to resemble π electrons. Such orbital cooperativity represents a new physical effect beyond the conventional Stark effect. Moreover, we have found that applying electric fields to the molecule would modify its molecular orbital diagram, depending on the directions of the electric fields; the electric field along the carbon-to-oxygen direction basically retains the MO diagram of the free CO molecule, with noticeable intra-orbital electron redistributions, whereas the oxygen-to-carbon electric field does create new states of molecular orbital contributions.

A quantitative, objective method for evaluating the surgical outcomes of baggy eyelid correction using orbital gray scale analysis

Baggy lower eyelids (BLEs) are a common cosmetic problem that is treated using various methods. However, validated objective methods for evaluating the treatment are limited. A novel BLE correction procedure, transconjunctival fat resection, and subsequent fat grafting, was assessed using the orbital gray scale (OGS), a previously suggested objective measure for BLEs. All patients were evaluated using both the tear trough rating scale (TTRS), a surgeon-derived evaluation method, and OGS, an objective computer-derived assessment. Changes throughout the surgery and their relationship to clinical characteristics, as well as the association between the two measurements, were statistically analyzed. A total of 50 patients who underwent surgery were analyzed. No major complications other than wrinkles were observed. All patients showed improvement in both the TTRS scores and OGS values (P<0.05). Lateral OGS was improved to a greater extent in older patients (P<0.05). Medial OGS change was associated with improvement of tear trough depression (P<0.05). Lateral OGS change was related to decreased infraorbital fat herniation (P<0.05). Total OGS change was related to improvement of both tear trough depression and fat prolapse (P<0.05). The total OGS change was significantly associated with improvements in tear trough depression and fat bulging. Therefore, it could be a convenient objective evaluation measure for eyelid correction procedures.

Millennial and orbital scale variability of the South American Monsoon during the penultimate glacial period

The presence of large, rapid climate oscillations is the most prominent feature of the Earth’s last glacial period. These oscillations are observed throughout the Northern Hemisphere and into the Southern Hemisphere tropics. Whether similar oscillations are typical of prior glacial periods, however, has not been well established. Here, we present results of a study of the South American Summer Monsoon system that covers nearly the entire penultimate glacial period, from 195 to 135 ky BP. We use a well-dated, high-resolution (~50 y) time series of oxygen isotopes to show that the precession of the earth’s orbit is the primary control on monsoon intensity. After removing the precession signal we observe millennial oscillations that are very similar in amplitude and structure to the Dansgaard/Oeschger cycles of the last interglacial and that match well a synthetic reconstruction of millennial variability. Time series analyses shows that the most prominent of the observed cycles occur at considerably longer frequency (~3500 y) that the Dansgaard/Oeschger cycles from Marine Isotope Stages 2–4.

Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions

Orbital binding energies in the ground state of many-electron elements obtained in experiments or in quantum-mechanical-calculations are studied. Their dependences on the atomic number and on the degree of ionization are analyzed. The Bohr – Sommerfeld semiclassical quantization condition is used and filled-shell orbital binding energy approximate scaling is shown. The scaling is similar to the one in the Thomas – Fermi model, but with two other functions-coefficients. The effective method of the demonstration of binding energies in a large number of atoms through these two functions is proposed. As a result, special features of the elements of the main and transition groups and the influence of relativistic effects are vividly manifested. Simple interpolation expressions are built for the two functions. One can use them to estimate orbital binding energies in the filled shells of many-electron atoms and ions to within 10% for middle elements and from 10% to 30% for heavy ones. The estimate can be used as the initial approximation in precessional atomic computations and also for rough calculations of the ionization cross sections of many-electron atoms and ions by electrons and heavy particles, failing more precise data.

Quantitative estimates of orbital and millennial scale climatic variability in central Mexico during the last ∼40,000 years

Diatom-based transfer functions for salinity, precipitation and temperature were developed using a training set that included data from 40 sites along central Mexico. These transfer functions showed good performance parameters and were subsequently applied to the previously published diatom record from lake Chalco, southern Basin of Mexico. Heinrich stadials (HS-3 to HS-0) were reconstructed as cold and dry events, with HS-2 representing the coldest and driest conditions, while HS-1 shows a complex bimodal cooling pattern. Orbital scale variability is also recorded. High and variable lake salinities from ∼34 to 29 ka BP (marine isotope stage 3, MIS-3) corresponded with times of maximum summer insolation and evidences of frequent fires. MIS-2 was identified as a cold period, with low lake salinity associated with low evaporation, with two cold intervals during the minima in spring (∼25.5 ka BP) and summer (∼20 ka BP) insolation. The ∼20 ka BP cold event together with HS-2 (24-23 ka BP), defined a bimodal maximum cooling during the last glacial maximum (LGM: 24.5–19.5 ka BP) within the range of pollen-based estimates, further supporting a maximum tropical cooling of 4–5 °C for the LGM. The deglacial (19.5–11.5 ka BP) showed the highest precipitation anomalies with three peaks that closely correlated with glacier advances in the nearby mountains (Iztaccihuatl). The early Holocene marked a change towards high lake salinities and the highest positive temperature anomalies (+3.5 °C) during a peak in summer insolation. Even though at orbital scale Chalco showed a nearly opposite trend to the record from the more southerly lake Peten-Itza (Guatemala), at millennial scale it showed a common pattern of cold and dry conditions during HSs, comparable to other tropical latitude sites in the northern hemisphere and further supporting the idea that there is a strong coupling between tropical and higher latitudes climates, in particular with the North Atlantic.

A stalagmite test of North Atlantic SST and Iberian hydroclimate linkages over the last two glacial cycles

Abstract. Close coupling of Iberian hydroclimate and North Atlantic sea surface temperature (SST) during recent glacial periods has been identified through the analysis of marine sediment and pollen grains co-deposited on the Portuguese continental margin. While offering precisely correlatable records, these time series have lacked a directly dated, site-specific record of continental Iberian climate spanning multiple glacial cycles as a point of comparison. Here we present a high-resolution, multi-proxy (growth dynamics and δ13C, δ18O, and δ234U values) composite stalagmite record of hydroclimate from two caves in western Portugal across the majority of the last two glacial cycles (∼220 ka). At orbital and millennial scales, stalagmite-based proxies for hydroclimate proxies covaried with SST, with elevated δ13C, δ18O, and δ234U values and/or growth hiatuses indicating reduced effective moisture coincident with periods of lowered SST during major ice-rafted debris events, in agreement with changes in palynological reconstructions of continental climate. While in many cases the Portuguese stalagmite record can be scaled to SST, in some intervals the magnitudes of stalagmite isotopic shifts, and possibly hydroclimate, appear to have been somewhat decoupled from SST.

“North-South” dipolar mode of precipitation changes in eastern China extends to the Last Deglaciation

Whether this observation imply that the ‘‘North-South” dipolar mode is no-longer applicable to the orbital scale needs to be further addressed using more high-quality precipitation records from both regions. Meanwhile, we also suggest that more attention should be paid to the development of high-resolution precipitation reconstructions since the Last Glacial/Interglacial from South China, which may help to resolve the issue of whether there is a ‘‘tripolar” mode of rainfall changes on various timescales over the eastern China. Such efforts could make a major contribution to our understanding of EASM dynamics, from a paleoclimatological perspective.

Laser space debris cleaning: elimination of detrimental self-focusing effects

A ground-based laser system for space debris cleaning requires pulse power well above the critical power for self-focusing in the atmosphere. Self-focusing results in beam quality degradation and is detrimental for the system operation. We demonstrate that, for the relevant laser parameters, when the thickness of the atmosphere is much less than the focusing length (that is, of the orbit scale), the beam transit through the atmosphere produces the phase distortion only. The model thus developed is in very good agreement with numerical modeling. This implies that, by using phase mask or adaptive optics, it may be possible to eliminate almost completely the impact of self-focusing effects in the atmosphere on the laser beam propagation.

Describing strong correlation with fractional-spin correction in density functional theory

An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.

Substitution effects on 1,3-disubstituted imidazol-2-ylidenes and 1,3-diarylimidazol-2-ylidenes revisited: a theoretical study at DFT level

Effect of substituents on philicity and stability of 1,3-disubstituted imidazol-2-ylidenes and 1,3-diarylimidazol-2-ylidenes was assessed using the following calculations: adiabatic electron affinity and adiabatic ionization potential, global electrophilicity and differential orbital energy scales for philicity, and ΔES–T, ΔEHyd, ΔEiso, and ΔEH–L for stability, with the aid of density functional theory and the results were then compared with each other. In the case of 1,3-disubstituted imidazol-2-ylidene, the carbene with CH3 group has the highest nucleophilic character considering all the above scales and the highest thermodynamic stability. 1,3-Diarylimidazol-2-ylidenes with CH3O and NH2 groups have high-nucleophilic properties and high-stability; their ΔEiso values are also greater than 377 kJ/mol which means that they may be reasonable synthetic targets. While, the presence of electron donating groups at 1,3-disubstituted imidazol-2-ylidene results in ΔEiso > 377 kJ/mol. Nucleophilicity of 1,3-diarylimidazol-2-ylidenes is, to some extent, greater than that of 1,3-disubstituted imidazol-2-ylidenes.

Dalangtan Saline Playa in a Hyperarid Region of Tibet Plateau: III. Correlated Multiscale Surface Mineralogy and Geochemistry Survey.

We report the first multiscale, systematic field-based testing of correlations between orbital scale advanced spaceborne thermal emission and reflection radiometer visible near-infrared (VNIR)/shortwave infrared (SWIR) reflectance and thermal infrared relative emissivity and outcrop scale Raman spectroscopy, VNIR reflectance, X-ray diffraction (XRD), and laser-induced breakdown spectroscopy (LIBS) mineralogy and chemistry in a saline dry lakebed. This article is one of three reports describing the evolution of salt deposits, meteorological record, and surface and subsurface salt mineralogy in Dalangtan, Qaidam Basin, a hyperarid region of the Tibet Plateau, China, as potential environmental, mineralogical, and biogeochemical analogs to Mars. We have successfully bridged remote sensing data to fine scale mineralogy and chemistry data. We have defined spectral end-members in the northwestern Qaidam Basin and classified areas within the study area on the basis of their spectral similarity to the spectral end-members. Results of VNIR/SWIR classification reveal zonation of spectral units within three large anticlinal domes in the study area that can be correlated between the three structures. Laboratory Raman, VNIR reflectance, XRD, and LIBS data of surface mineral samples collected along a traverse over Xiaoliangshan (XLS) indicate that the surface is dominated by gypsum, Mg sulfates, Na sulfates, halite, and carbonates, with minor concentrations of illite present in most samples as well. Our results can be used as a first step toward better characterizing the potential of orbital reflectance spectroscopy as a method for mineral detection and quantification in salt-rich planetary environments, with the benefit that this technique can be validated on the ground using instruments onboard rovers.

Stability of the Nagaoka-type ferromagnetic state in a t2g orbital system on a cubic lattice

We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three dimensional $t_{2g}$-orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals, which allow two-dimensional hopping within each orbital plane. In the strong coupling limit of $U\to \infty$, the orbital-generalized Nagaoka ferromagnetic states are proved degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than $L^{\frac{1}{2}}$. This result is valid for arbitrary values of the ferromagnetic Hund's coupling $J>0$ and inter-orbital repulsion $V\ge 0$. The stability of the Nagaoka-type state at finite electron densities with respect to a single spin-flip is investigated. These results provide helpful guidance for studying the mechanism of itinerant ferromagnetism for the $t_{2g}$-orbital materials.

Orbital scale lake evolution in the Ejina Basin, central Gobi Desert, China revealed by K-feldspar luminescence dating of paleolake shoreline features

The Ejina Basin in the central Gobi Desert contains the terminal lakes of the Heihe River. Paleoenvironmental changes in the basin are important since its deposits are a significant source of Northern Hemisphere dust. In this study we employed a K-feldspar pIRIR dating technique to date shoreline features ≥940 m at multiple locations in the Ejina Basin ∼45–50 m above the modern basin floor. Internal checks of luminescence characteristics were employed to test the reliability of the pIRIR dating. In combination with our previously reported stratigraphy and chronology of shorelines at ≤927 m in the Ejina Basin, these results imply that a paleolake was present in the basin prior to ∼350 ka. Other high stands in the basin occurred at ∼320-310 ka, 240-180 ka, 120-80 ka, and ∼5 ka, corresponding to MIS 9, MIS 7, MIS 5 and the mid Holocene (MIS 1), respectively, indicating a strong link with glacial-interglacial cycles. Extensions of the East Asian Summer Monsoon (EASM) during interglacial periods, possibly interacting with the Westerlies, apparently caused higher precipitation and lake formation. The impact of orbital eccentricity on the EASM/Westerlies appears to be responsible for the formation of major lake/desert cycles on the northeastern margin of the Tibetan Plateau.

Hierarchical Bayesian calibration of tidal orbit decay rates among hot Jupiters

Transiting hot Jupiters occupy a wedge-shaped region in the mass ratio-orbital separation diagram. Its upper boundary is eroded by tidal spiral-in of massive, close-in planets and is sensitive to the stellar tidal dissipation parameter $Q_s'$. We develop a simple generative model of the orbital separation distribution of the known population of transiting hot Jupiters, subject to tidal orbital decay, XUV-driven evaporation and observational selection bias. From the joint likelihood of the observed orbital separations of hot Jupiters discovered in ground-based wide-field transit surveys, measured with respect to the hyperparameters of the underlying population model, we recover narrow posterior probability distributions for $Q_s'$ in two different tidal forcing frequency regimes. We validate the method using mock samples of transiting planets with known tidal parameters. We find that $Q_s'$ and its temperature dependence are retrieved reliably over five orders of magnitude in $Q_s'$. A large sample of hot Jupiters from small-aperture ground-based surveys yields $\log_{10} Q_s'=(8.26\pm 0.14)$ for 223 systems in the equilibrium-tide regime. We detect no significant dependence of $Q_s'$ on stellar effective temperature. A further 19 systems in the dynamical-tide regime yield $\log_{10} Q_s'=7.3\pm 0.4$, indicating stronger coupling. Detection probabilities for transiting planets at a given orbital separation scale inversely with the increase in their tidal migration rates since birth. The resulting bias towards younger systems explains why the surface gravities of hot Jupiters correlate with their host stars' chromospheric emission fluxes. We predict departures from a linear transit-timing ephemeris of less than 4 seconds for WASP-18 over a 20-year baseline.

A MIS 9/MIS 8 speleothem record of hydrological variability from Macedonia (F.Y.R.O.M.)

The period corresponding to Marine Isotope Stages 9 (MIS 9) offers the opportunity to study orbital and sub-orbital scale climate variability under boundary conditions different from those of better studied intervals such as the Holocene and the Last Interglacial. Yet, it is poorly represented in independently-dated continental archives around the Mediterranean Region. Here, we present a speleothem stable isotope record (δ18O and δ13C) from the Former Yugoslavian Republic of Macedonia (F.Y.R.O.M., southern Balkans), which consists of two periods of growth broadly covering the ca. 332 to 292 ka and the ca. 264 to 248 ka intervals (MIS 9e-b and late MIS 8). We interpret the speleothem δ18O as mostly related to regional hydrology, with variations that can be interpreted as due to changes in rainfall amount, with higher/lower values associated to drier/wetter condition. This interpretation is corroborated by a change in mineralogical composition between aragonite and calcite at ca. 328 ka, which marks increasing precipitation at the onset of MIS 9 and occurs within a trend of decreasing δ18O values. Also the comparison with the multiproxy climate record available from the nearby Lake Ohrid seems to support the proposed interpretation. The MIS 9e interglacial appears to be characterized by wettest conditions between ca. 326 and 321 ka, i.e. lasting ca. 5 kyr. Decreasing precipitation and enhanced millennial scale variability matches the glacial inception (MIS9 d to b), with drier events at ca. 319 ka (ca. 2 kyr long) and 310 ka (ca. 1 kyr long), and a major rainfall reduction between 306 and 298 ka. The latter is followed by a prominent wetter period between 298 and 295 ka, for which carbon data values suggest high infiltration rate. Rainfall decreases again after 295 ka, and remain low until the growth interruption at ca. 292 ka. Resumption of the growth and progressive soil development, expressed by the carbon isotope record, occurred during the late part of MIS 8. Despite the rather high temporal uncertainty (average 6 ka), the speleothem hydrological record complements the environmental information provided by the Lake Ohrid record and also fits well to the framework of regional and extra-regional variability, showing similarities with pollen records from southern and western Europe, both at orbital and at sub-orbital time scale.

Vegetation and climate reconstructions on different time scales in China: a review of Chinese palynological research

This paper reviews vegetation and climate reconstructions for different time scales based on palynological studies in China. It discusses examples of significant developments in palynological research topics within China: (1) Modern pollen—a modern pollen database (East Asia Surface Pollen Database) has been established through the collaboration of Chinese palynologists. Based on these data, modern pollen distributions and their quantitative relationship with vegetation and climate have been thoroughly studied. (2) Pre-Quaternary vegetation and climate dynamics—scientists have mapped pollen and palaeobotanical data from the Palaeogene. The vegetation distributions confirm a north–south zonal pattern during the Palaeogene that changed to an east–west monsoonal pattern during the Miocene and Pliocene. These results provide key evidence for understanding monsoon evolution. (3) Late-Quaternary vegetation—biome reconstructions based on fossil pollen data show spatial and temporal changes in vegetation since the Last Glacial Maximum, permitting a better understanding of climate change across China. (4) Quantitative climate reconstructions—some reconstructions have successfully detected Holocene climate variability thereby providing insights into monsoon history. At present, there are no comprehensive spatial reconstructions. Major possible future developments should focus on: (1) long-term vegetation reconstructions from lakes to study Asian monsoon dynamics at orbital scales; (2) quantitative reconstructions of vegetation and climate change to help stronger integration with palaeoclimate models and dynamic vegetation models; (3) land-cover and land-use change across China over the last 6,000 years to understand human impacts and provide empirical data for climate modellers; and (4) integration of pollen data with vegetation and climate modelling to understand the CO2-vegetation relationship and climate dynamics.

Distribution and ecology of the Globigerinoides ruber — Globigerinoides elongatus morphotypes in the Azores region during the late Pleistocene-Holocene

Globigerinoides ruber is the dominant taxon in the North Atlantic Subtropical Gyre, nowadays limited to the north by the Azores Current. It is highly sensitive to recent and late Pleistocene Azores Front Current System variability. In this study, we analyse the distribution of five individual morphotypes of the G. ruber – G. elongatus plexus (G. ruber s.s., G. ruber cyclostoma type, G. elongatus, G. elongatus cf.1, G. elongatus pyramidical type) and G. ruber kummerform gr. in a core (ATA13-OF-KT1) collected southwest of the Azores islands and located in a strategical position near the present-day boundary of the Subtropical Gyre/Azores Front Current System (STG/AFCS). Micropaleontological and stable isotope analyses can provide new insights on the ecological preferences of the G. ruber chromotypes and some selected morphotypes (especially the less studied G. ruber cyclostoma type). Their distribution pattern shows cyclic oscillations linked to climatic variability at orbital and millennial scales. G. elongatus clearly dominated the G. ruber - G. elongatus assemblage during the interglacials, while G. ruber cyclostoma type reached their maxima abundances during glacial periods. Furthermore, changes in the relative abundance of warm (G. elongatus) and cool water (G. ruber cyclostoma type) morphotypes represent a powerful tool to track the position occupied by the Subtropical Gyre/Azores Current (STG/AC) boundary during the last 74.7kyr.

Assessment of age- and sex-related changes in baggy lower eyelids using a novel objective image analysis method: Orbital gray scale analysis.

Baggy lower eyelids (BLEs) are a common aesthetic problem of aging. Valid and reliable assessment tools for BLEs are required to evaluate the current status and treatment outcome. Age- and sex-related changes in BLEs were assessed with the orbital gray scale (OGS), a novel objective image analysis method. We gathered frontal-view photographs of the faces of the patients who sought for correction of BLEs. Based on the clinical pattern, we classified the BLEs of the subjects into medial (M), medial and central (MC), and medial to lateral (MCL) types. Severity was evaluated using the OGS, a modified method of the linear gray scale analysis. The BLEs of 1034 subjects were classified. The most common types were MCL type in the men and MC type in the women, respectively. The M and MC types were common in the young subjects, whereas the MCL type was more common in the old subjects (P<.001). The measurements of OGS in 104 subjects showed positive correlation with age, a higher mean value in the men, and a trend toward higher values in the order of M, MC, and MCL types (P<.001 for central and lateral OGS scores). In a multiple linear regression analysis, central and lateral OGS values were significantly related with age, sex, and M-C-L classification type (P<.001). The M-C-L classification and OGS were significantly associated with both age and sex, proving that they could be potent objective assessment tools for BLEs.

Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations

AbstractThe delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC–DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.