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At least 271 records · Page 15

Energetics of molecular-beam epitaxy models

The removal energies of constituent atoms from various unreconstructed semiconductor surfaces are calculated using a Green function method. An efficient difference-equation approach within the second-neighbor tight-binding model is employed. For a compound AB, binding energies for the A and B atoms on the (111), (-1 -1 -1), (100), and (110) surfaces are calculated. Analyses are made of the energy to remove an atom from the nearly full surface and from the nearly empty surface. Results are presented for Si, GaAs, CdTe, and HgTe; and the surface sublimation energies are found to depend on surface coverage and do not display a simple linear relationship to the number of bonds broken, as is often assumed in modeling growth by MBE.

Krishnamurthy, Srinivasan↗

Preparation and Thermoelectric Properties of the Skutterudite-Related Phase Ru(0.5)Pd(0.5)Sb3

A new skutterudite phase Ru(0.5)Pd(0.5)Sb3 was prepared. This new phase adds to a large number of already known materials with the skutterudite structure which have shown good potential for thermoelectric applications. Single phase, polycrystalline samples were prepared and characterized by x-ray analysis, electron probe microanalysis, density, sound velocity, thermal-expansion coefficient, and differential thermal analysis measurements. Ru(0.5)Pd(0.5)Sb3 has a cubic lattice, space group Im3 (T(sup 5, sub h)), with a = 9.298 A and decomposes at about 920 K. The Seebeck coefficient, the electrical resistivity, the Hall effect, and the thermal conductivity were measured on hot-pressed samples over a wide range of temperatures. Preliminary results show that Ru(0.5)Pd(0.5)Sb3 behaves as a heavily doped semiconductor with an estimated band gap of about 0.6 eV. The lattice thermal conductivity of Ru(0.5)Pd(0.5)Sb3 is substantially lower than that of the binary isostructural compounds CoSb3 and IrSb3. The unusually low thermal conductivity might be explained by additional hole and charge transfer phonon scattering in this material. The potential of this material for thermoelectric applications is discussed.

Caillat, T.↗

Profile Evolution Simulation in Etching Systems Using Level Set Methods

Semiconductor device profiles are determined by the characteristics of both etching and deposition processes. In particular, a highly anisotropic etch is required to achieve vertical sidewalls. However, etching is comprised of both anisotropic and isotropic components, due to ion and neutral fluxes, respectively. In Ar/Cl2 plasmas, for example, neutral chlorine reacts with the Si surfaces to form silicon chlorides. These compounds are then removed by the impinging ion fluxes. Hence the directionality of the ions (and thus the ion angular distribution function, or IAD), as well as the relative fluxes of neutrals and ions determines the amount of undercutting. One method of modeling device profile evolution is to simulate the moving solid-gas interface between the semiconductor and the plasma as a string of nodes. The velocity of each node is calculated and then the nodes are advanced accordingly. Although this technique appears to be relatively straightforward, extensive looping schemes are required at the profile corners. An alternate method is to use level set theory, which involves embedding the location of the interface in a field variable. The normal speed is calculated at each mesh point, and the field variable is updated. The profile comers are more accurately modeled as the need for looping algorithms is eliminated. The model we have developed is a 2-D Level Set Profile Evolution Simulation (LSPES). The LSPES calculates etch rates of a substrate in low pressure plasmas due to the incident ion and neutral fluxes. For a Si substrate in an Ar/C12 gas mixture, for example, the predictions of the LSPES are identical to those from a string evolution model for high neutral fluxes and two different ion angular distributions.(2) In the figure shown, the relative neutral to ion flux in the bulk plasma is 100 to 1. For a moderately isotropic ion angular distribution function as shown in the cases in the left hand column, both the LSPES (top row) and rude's string method (bottom row) predict tapered profiles. The LSPES uses an AD with a FWHM = 13.5 degrees, and rude's model uses a ratio of sheath voltage to ion temperature of 50. The more anisotropic IADs produce profiles with more vertical sidewalls and a wider bottom surface, as shown in the right hand column. Here, the LSPES has an AD with a FWHM = 2 degrees, and rude's model uses a ratio of 500 of sheath voltage to ion temperature. The agreement between the LSPES and rude's model is excellent in both cases. We will present etching profiles generated by the LSPES, including calculations of the re-emitted fluxes of both neutrals and ions off of the profile walls. In addition, we will show the effect of geometric structures (overhangs, etc.) on the etching profiles. Other physical aspects, such as surface diffusion, will also be included in the model.

Hwang, Helen H.↗

Impacts of Non-Ideal Back Contact on Capacitance Measurements in CdTe Solar Cells

CdTe solar cells suffer from a non-ideal back contact which can strongly affect the equivalent circuit model and complicate capacitance measurements. Here, five different back contact materials are deposited on identical CdTe absorbers and their influence on capacitance measurements is characterized. A five-element equivalent circuit model is shown to represent a CdTe solar cell with a non-ideal back contact, and capacitance-frequency (C-f) measurements on each sample clearly show the influence of this contact. Capacitance-voltage (C-V) measurements on each sample show the influence of frequency on measured capacitance. In the AlGaOx/Au sample, temperature dependent C-fs show the back barrier height to be 240 meV, and ongoing measurements will give a comparison of back barrier heights for all samples. This study provides insight into the efficacy of various back contacts and highlights potential errors in the interpretation of capacitance measurements due to the presence of the back contact.

cadmium compounds↗

High-Performance Thermoelectric Semiconductors

Figures of merit almost double current state-of-art thermoelectric materials. IrSb3 is semiconductor found to exhibit exceptional thermoelectric properties. CoSb3 and RhSb3 have same skutterudite crystallographic structure as IrSb3, and exhibit exceptional transport properties expected to contribute to high thermoelectric performance. These three compounds form solid solutions. Combination of properties offers potential for development of new high-performance thermoelectric materials for more efficient thermoelectric power generators, coolers, and detectors.

Fleurial, Jean-Pierre↗

Disordered Zinc in Zn4Sb3 with Phonon-Glass and Electron-Crystal Thermoelectric Properties

By converting waste heat into electricity, thermoelectric generators could be an important part of the solution to today's energy challenges. The compound Zn4Sb3 is one of the most efficient thermoelectric materials known. Its high efficiency results from an extraordinarily low thermal conductivity in conjunction with the electronic structure of a heavily doped semiconductor. Previous structural studies have been unable to explain this unusual combination of properties. Here, we show through a comprehensive structural analysis using single-crystal X-ray and powder-synchrotron-radiation diffraction methods, that both the electronic and thermal properties of Zn4Sb3 can be understood in terms of unique structural features that have been previously overlooked. The identification of Sb3- ions and Sb-2(4-) dimers reveals that Zn4Sb3 is a valence semiconductor with the ideal stoichiometry Zn13Sb10. In addition, the structure contains significant disorder, with zinc atoms distributed over multiple positions. The discovery of glass-like interstitial sites uncovers a highly effective mechanism for reducing thermal conductivity. Thus Zn4Sb3 is in many ways an ideal 'phonon glass, electron crystal' thermoelectric material.

phases↗

Nano-Ceramic Coated Plastics

Plastic products, due to their durability, safety, and low manufacturing cost, are now rapidly replacing cookware items traditionally made of glass and ceramics. Despite this trend, some still prefer relatively expensive and more fragile ceramic/glassware because plastics can deteriorate over time after exposure to foods, which can generate odors, bad appearance, and/or color change. Nano-ceramic coatings can eliminate these drawbacks while still retaining the advantages of the plastic, since the coating only alters the surface of the plastic. The surface coating adds functionality to the plastics such as self-cleaning and disinfectant capabilities that result from a photocatalytic effect of certain ceramic systems. These ceramic coatings can also provide non-stick surfaces and higher temperature capabilities for the base plastics without resorting to ceramic or glass materials. Titanium dioxide (TiO2) and zinc oxide (ZnO) are the candidates for a nano-ceramic coating to deposit on the plastics or plastic films used in cookware and kitchenware. Both are wide-bandgap semiconductors (3.0 to 3.2 eV for TiO2 and 3.2 to 3.3 eV for ZnO), so they exhibit a photocatalytic property under ultraviolet (UV) light. This will lead to decomposition of organic compounds. Decomposed products can be easily washed off by water, so the use of detergents will be minimal. High-crystalline film with large surface area for the reaction is essential to guarantee good photocatalytic performance of these oxides. Low-temperature processing (<100 C) is also a key to generating these ceramic coatings on the plastics. One possible way of processing nanoceramic coatings at low temperatures (< 90 C) is to take advantage of in-situ precipitated nanoparticles and nanostructures grown from aqueous solution. These nanostructures can be tailored to ceramic film formation and the subsequent microstructure development. In addition, the process provides environment- friendly processing because of the aqueous solution. Low-temperature processing has also shown versatility to generate various nanostructures. The growth of low-dimensional nanostructures (0-D, 1-D) provides a means of enhancing the crystallinity of the solution-prepared films that is of importance for photocatalytic performance. This technology can generate durable, fully functional nano-ceramic coatings (TiO2, ZnO) on plastic materials (silicone, Teflon, PET, etc.) that can possess both photocatalytic oxide properties and flexible plastic properties. Processing cost is low and it does not require any expensive equipment investment. Processing can be scalable to current manufacturing infrastructure.

Cho, Junghyun↗

Design of a three-layer antireflection coating for high efficiency indium phosphide solar cells using a chemical oxide as first layer

It is well known that the behavior of III-V compound based solar cells is largely controlled by their surface, since the majority of light generated carriers (63% for GaAs and 79% for InP) are created within 0.2 mu m of the surface of the illuminated cell. Consequently, the always observed high surface recombination velocity (SRV) on these cells is a serious limiting factor for their high efficiency performance, especially for those with p-n junction made by either thermal diffusion or ion implantation. A good surface passivation layer, ideally a grown oxide as opposed to a deposited one, will cause a significant reduction in the SRV without adding interface problems, thus improving the performance of III-V compound based solar cells. Another significant benefit to the overall performance of the solar cells can be achieved by a substantial reduction of their large surface optical reflection by the use of a well designed antireflection (AR) coating. In this paper, we demonstrate the effectiveness of using a chemically grown thermally and chemically stable oxide, not only for surface passivation but also as an integral part of a 3-layer AR coating for thermally diffused p+n InP solar cells. A phosphorus-rich interfacial oxide, In(PO3)3, is grown at the surface of the p+ emitter using an etchant based on HNO3, o-H3PO4 and H2O2. This oxide has the unique properties of passivating the surface as well as serving as an efficient antireflective layer yielding a measured record high AMO open-circuit voltage of 890.3 mV on a thermally diffused InP(Cd,S) solar cell. Unlike conventional single layer AR coatings such as ZnS, Sb2O3, SiO or double layer AR coatings such as ZnS/MgF2 deposited by e-beam or resistive evaporation, this oxide preserves the stoichiometry of the InP surface. We show that it is possible to design a three-layer AR coating for a thermally diffused InP solar cell using the In(PO3)3 grown oxide as the first layer and Al2O3 and MgF2 as the second and third layers respectively, so as to yield an overall theoretical reflectance of less than 2%. Since chemical oxides are readily grown on III-V semiconductors materials, the technique of using the grown oxide layer to both passivate the surface as well as serve as the first of a multilayer AR coating should work well for all III-V compound-based solar cells.

Moulot, Jacques↗

Utilization of Novel (KNbO 3 ) 1− x (Ba 2 FeNbO 6 ) x ( x = 0.1, 0.2, 0.3) Solid Solutions for Efficient Photo‐Assisted Fenton Degradation of Methylene Blue Dye

Novel (KNbO 3 ) 1− x (Ba 2 FeNbO 6 ) x ( x = 0.1, 0.2, 0.3) solid solutions corresponding to K 0.82 Ba 0.18 Fe 0.09 Nb 0.91 O 3 , K 0.64 Ba 0.36 Fe 0.18 Nb 0.82 O 3 , and K 0.46 Ba 0.54 Fe 0.27 Nb 0.73 O 3 compounds have been synthesized via molten salt method. X‐ray diffraction confirms the formation of solid solutions, while transmission electron microscopy combined with energy‐dispersive spectroscopy results demonstrates a homogeneous distribution of elements. The obtained solid solutions crystallized in a cubic crystal structure, whereas the parent KNbO 3 possesses an orthorhombic structure. The wide bandgap semiconductor KNbO 3 transformed into a visible‐light‐active material, with its bandgap energy reduced from 3.56 eV to ≈2.4 eV. The substitution of K in KNbO 3 with Ba is responsible for structural modification from orthorhombic to cubic symmetry, whereas both structural modification and the substitution of Nb with Fe correlated with optical properties. The photocatalytic activities of all obtained solid solutions are improved compared with the parent KNbO 3 and Ba 2 FeNbO 6 compounds for photocatalytic degradation of methylene blue (MB) dye. Among the series of solid solutions, K 0.82 Ba 0.18 Fe 0.09 Nb 0.91 O 3 photocatalysts show the highest MB removal efficiency owing to its relatively higher surface area, suppressed charge carrier recombination, and more negative conduction band edge. Moreover, K 0.82 Ba 0.18 Fe 0.09 Nb 0.91 O 3 photocatalyst (0.1 g) combined with hydrogen peroxide (H 2 O 2 ) to form a novel photo‐Fenton system, achieving almost complete degradation of 100 mL of 10 mg L −1 MB dye in 30 min.

Avcıoğlu, Celal [Technische Universität Berlin, Fa↗

Semiconductor photoelectrochemistry

Semiconductor photoelectrochemical reactions are investigated. A model of the charge transport processes in the semiconductor, based on semiconductor device theory, is presented. It incorporates the nonlinear processes characterizing the diffusion and reaction of charge carriers in the semiconductor. The model is used to study conditions limiting useful energy conversion, specifically the saturation of current flow due to high light intensity. Numerical results describing charge distributions in the semiconductor and its effects on the electrolyte are obtained. Experimental results include: an estimate rate at which a semiconductor photoelectrode is capable of converting electromagnetic energy into chemical energy; the effect of cell temperature on the efficiency; a method for determining the point of zero zeta potential for macroscopic semiconductor samples; a technique using platinized titanium dioxide powders and ultraviolet radiation to produce chlorine, bromine, and iodine from solutions containing their respective ions; the photoelectrochemical properties of a class of layered compounds called transition metal thiophosphates; and a technique used to produce high conversion efficiency from laser radiation to chemical energy.

Buoncristiani, A. M.↗

Design of a Three-Layer Antireflection Coating for High Efficiency Indium Phosphide Solar Cells Using a Chemical Oxide as First Layer

It is well known that the behavior of III-V compound based solar cells is largely controlled by their surface, since the majority of light generated carriers (63% for GaAs and 79% for InP) are created within 0.2 microns of the illuminated surface of the cell. Consequently, the always observed high surface recombination velocity (SRV) on these cells is a serious limiting factor for their high efficiency performance, especially for those with the p-n junction made by either thermal diffusion or ion implantation. A good surface passivation layer, ideally, a grown oxide as opposed to a deposited one, will cause a significant reduction in the SRV without adding interface problems, thus improving the performance of III-V compound based solar cells. Another significant benefit to the overall performance of the solar cells can be achieved by a substantial reduction of their large surface optical reflection by the use of a well designed antireflection (AR) coating. In this paper, we demonstrate the effectiveness of using a chemically grown, thermally and chemically stable oxide, not only for surface passivation but also as an integral part of a 3- layer AR coating for thermally diffused p(+)n InP solar cells. A phosphorus-rich interfacial oxide, In(PO3)3, is grown at the surface of the p(+) emitter using an etchant based on HNO3, o-H3PO4 and H2O2. This oxide has the unique properties of passivating the surface as well as serving as a fairly efficient antireflective layer yielding a measured record high AM0, 25 C, open-circuit voltage of 890.3 mV on a thermally diffused InP(Cd,S) solar cell. Unlike conventional single layer AR coatings such as ZnS, Sb2O3, SiO or double layer AR coatings such as ZnS/MgF2 deposited by e-beam or resistive evaporation, this oxide preserves the stoichiometry of the InP surface. We show that it is possible to design a three-layer AR coating for a thermally diffused InP solar cell using the In(PO3)3 grown oxide as the first layer and Al2O3, MgF2 or ZnS, MgF2 as the second and third layers respectively, so as to yield an overall theoretical reflectance of less than 2%. Since chemical oxides are readily grown on III-V semiconductor materials, the technique of using the grown oxide layer to both passivate the surface as well as serve as the first of a multilayer AR coating, should work well for essentially all III-V compound-based solar cells.

Moulot, Jacques↗

Defect-Limited Mobility and Defect Thermochemistry in Mixed A-Cation Tin Perovskites: (CH3NH3)1-xCsxSnBr3

Hybrid organic-inorganic semiconductors crystallizing in the perovskite structure present a significant opportunity for realizing defect-tolerant semiconductors. In this work, we examine the solid solution, (CH3NH3)1-xCsxSnBr3, and identify the thermochemistry dictating the intrinsic carrier concentrations and how local structural distortions influences this electronic behavior. This family of compounds exhibits the expected systematic trend in decreasing optical gap with the cesium to methylammonium A-site mixing ratio, x, in the visible region. However, the carrier mobility, as determined from time-resolved microwave conductivity measurements, trends opposite to that expected from first-principles calculations combined with Boltzmann scattering theory calculations of the carrier mobility. We propose that this is a result of increasing carrier scattering with x in (CH3NH3)1-xCsxSnBr3 due to a significant increase in the carrier density with x. By examining the dependence of the carrier density as a function of x, we infer the compositional-dependence of the average enthalpy and nonconfigurational entropy per defect. While diffraction reveals a cubic aristotypic perovskite structure as a function of x at room temperature, the pair distribution functions obtained from synchrotron X-ray total scattering from these materials are better described by symmetry-adapted displacement modes of the Pm3m crystal structure, which we attribute to a large degree of anharmonic dynamics of the atom positions. This analysis shows that CH3NH3+-rich compositions retain mostly linear Sn-Br-Sn bonding environments through the displacements, while Cs+-rich compositions lead to more significantly bent Sn-Br-Sn environments. We propose that these bent bonding arrangements in Cs-rich compositions yield a higher propensity for defect formation. This also provides a rationale for carrier trapping that gives rise to anomalous microwave transients. Together, these results provide insight into the structure-dynamics-properties relationships in this highly anharmonic system with high amplitude atomic motions and low defect formation energies.

defect thermochemistry↗

Growing Organic Crystals By The Czochralski Method

Apparatus grows high-quality single crystals of organic compounds by Czochralski method. In Czochralski process, growing crystal lifted from middle of molten material without touching walls. Because of low melting temperatures of organic crystals, glass vessels usable. Traditional method for inorganic semiconductors adapted to optically nonlinear organic materials.

Shields, Angela↗

Characterization of PVT Grown ZnSe by Low Temperature Photoluminescence

ZnSe, a II-VI semiconductor with a large direct band gap of 2.7 eV at room temperature and 2.82 eV at 10 K, is considered a promising material for optoelectric applications in the blue-green region of the spectrum. Photoemitting devices and diode laser action has been demonstrated as a result of decades of research. A key issue in the development of II-VI semiconductors is the control of the concentration of the various impurities. The II-VI semiconductors seem to defy the effort of high level doping due to the well known self compensation of the donors and the acceptors. A good understanding of roles of the impurities and the behavior of the various intrinsic defects such as vacancies, interstitials and their complexes with impurities is necessary in the development and application of these materials. Persistent impurities such as Li and Cu have long played a central role in the photoelectronic properties of many II-VI compounds, particularly ZnSe. The shallow centers which may promote useful electrical conductivity are of particular interest. They contribute the richly structured near gap edge luminescence, containing weak to moderate phonon coupling and therefore very accessible information about the energy states of the different centers. Significance of those residual impurities which may contribute such centers in II-VI semiconductors must be fully appreciated before improved control of their electrical properties may be possible. Low temperature photoluminescence spectroscopy is an important source of information and a useful tool of characterization of II-VI semiconductors such as ZnSe. The low temperature photoluminescence spectrum of a ZnSe single crystal typically consists of a broad band emission peaking at 2.34 eV, known as the Cu-green band, and some very sharp lines near the band gap. These bands and lines are used to identify the impurity ingredients and the defects. The assessment of the quality of the crystal based on the photoluminescence analysis is then possible. In this report we present the characterization of a ZnSe single crystal as grown by the physical vapor transport method, with special intention paid to the possible effects of the gravitational field to the growth of the crystal.

Wang, Ling Jun↗

When Pore Met Semi: Charting the Rise of Porous Metal Halide Semiconductors

Metal halide semiconductors (MHS) are a versatile class of materials with fully customizable mechanical and optoelectronic properties that have proven to be prominent candidates in numerous impactful applications. Finding a way to generate porosity in MHS would bestow upon them an additional node in property engineering, thus allowing them to be utilized in uncharted technologies. Motivated by this promise, we developed a general strategy to render the MHS porous. We employed molecular cages as structure-directing agents and countercations, which fostered a new family of materials: porous metal halide semiconductors (PMHS). The presence of molecular cages gave rise to ultramicroporous structures imposed by the organic part cavities and a record water stability performance of 27 months so far. In this Perspective, we discuss the principles and promises of PMHS, which combine the merits of porous and electronic compounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Apparatus for use in examining the lattice of a semiconductor wafer by X-ray diffraction

An improved apparatus for examining the crystal lattice of a semiconductor wafer utilizing X-ray diffraction techniques was presented. The apparatus is employed in a method which includes the step of recording the image of a wafer supported in a bent configuration conforming to a compound curve, produced through the use of a vacuum chuck provided for an X-ray camera. The entire surface thereof is illuminated simultaneously by a beam of incident X-rays which are projected from a distant point-source and satisfy conditions of the Bragg Law for all points on the surface of the water.

Parker, D. L.↗

Studies on organic semiconductors. 15: Effects of the substituents on the photoconductivities of substituted anthracenes

The photocurrents of the substituted anthracenes, 1,5-diacetylanthracene (2), 1-acetylanthracene (3), 9-acetylanthracene (4), 1,5-dichloroanthracene (5), 1,5-diethylanthracene (6), 1,5-dimethoxyanthracene (7), 9-cyanoanthracene (8), and anthracene (1) were measured by using their surface type cells in nitrogen. The compounds of (1), (5), (6), (7), and (8) showed the photocurrent spectra which corresponded to the absorption spectra of their evaporated films. In the cases of (2) and (3), however, the anomalous photocurrent appeared in the threshold region of their absorption spectra. The appearance of the anomalous photocurrent was characteristic of anthracenes having the acetyl group at 1- and/or 5-position. The magnitude of the photocurrents of the 1,5-disubstituted anthracenes was similar to that of (1). The photocurrents of the monosubstituted anthracenes were smaller than that of (1). Among the monosubstituted anthracenes, the compound (4) showed no photocurrent under the same conditions. Contrary to the results obtained in the cases of phenazines, the photoconductivities of the anthracene derivatives became better in air.

Sugimoto, A.↗

An improved guess for the variational calculation of charge-transfer excitations in large systems

Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.

Bogo, Nicola↗