Core Hole Research Articles

Evaluating propensity for fugitive gas migration from integrity compromised oil and gas wells in the Peace Region, British Columbia, Canada, with a petrophysical approach

Oil and gas wells can suffer integrity failure resulting in the release of fugitive gas, formed primarily of methane, into the subsurface and atmosphere. Factors affecting fugitive gas migration in the subsurface, and in particular within and between shallower units intersected by energy wells (i.e. <100 m depth), are usually poorly considered with little focus on specific lithological characteristics that control gas movement, determine environmental impacts and influence how best to detect, monitor and quantify fugitive gases. To better understand and identify properties that can control fugitive gas migration in shallow sedimentary rocks that form the Peace Region of British Columbia, Canada, we developed a workflow by which a series of rock cores from units present in the area were obtained and their flow properties characterised. Insights on propensity for fugitive gas migration within and between these rocks were achieved through laboratory techniques and analytical calculations that are usually applied to the study of deeper hydrocarbon migration and seal integrity. These included Mercury Intrusion Porosimetry, petrographic analysis, X-ray computed tomography, as well as estimations of threshold capillary pressure, gas-column heights, hydrostatic pore pressure and total displacement pressure. Results show a congruent correlation between the examined petrophysical rock characteristics and flow propensity. We find that high capillary pressure will act as an effective mechanism for limiting vertical gas migration in the region, even when potential barrier facies have porosities of more than 10% and permeability of 0.26 mD. Additionally, results suggest that the propensity of studied shallow sediments to transmit fugitive gases will be controlled by heterogeneity, permeability anisotropy and the presence of secondary structural features, such as microfractures. Our approach for evaluating the propensity of fugitive gas migration could be applied elsewhere to enhance understanding of potential migration pathways and aid in development of effective monitoring and detection strategies that can better anticipate gas behaviour in the subsurface and prognosticate reactive transport, impacts and fate.

Direct displacement-based design of SEDRC systems considering higher mode effects

Self-centering energy-absorbing dual rocking core (SEDRC) system was recently proposed for obtaining damage-free performance under design earthquakes or low damage under extreme earthquakes in steel building structures. Although the SEDRC system can mainly deform based on the fundamental mode shape, the higher modes may significantly impact the structural element forces. This research intends to investigate the effects of higher mode on the seismic performance and structural member force demands of the SEDRC system under earthquakes and propose a performance-based design (PBD) method considering the higher mode effects. The formulation for calculating the design base shear pondering the influence of higher mode is deduced. The detailed design steps and equations for calculating the force demands of structural members are presented. Three archetypes, including nine-, fifteen-, and twenty-story SEDRC systems, respectively, are designed according to the PBD method. Moreover, the other six corresponding archetypes are designed according to the previous design process without consideration of higher mode effects as comparative buildings. Nonlinear dynamic analyses were performed to evaluate the seismic responses of the designed structures. The analysis results validate the high precision of the proposed methodology in designing multi-story to high-rise SEDRC systems.

Theory of x-ray absorption spectroscopy: A microscopic Bloch equation approach for two-dimensional solid states

We develop a self-consistent Maxwell-Bloch formalism for the interaction of x-rays with two-dimensional crystalline materials by incorporating the Bloch theorem and Coulomb many-body interaction. This formalism is illustrated for graphene, by calculating the polarization-dependent XANES, formulating expressions for the radiative and Meinter-Auger recombination of core holes, and the discussion of microscopic insights into the spectral oscillations of EXAFS beyond point scattering theory. In particular, the correct inclusion of lattice periodicity in our evaluation allows us to assign so far uninterpreted spectral features in the Fourier transformed EXAFS spectrum.

How to improve machine learning models for lithofacies identification by practical and novel ensemble strategy and principles

Typically, relationship between well logs and lithofacies is complex, which leads to low accuracy of lithofacies identification. Machine learning (ML) methods are often applied to identify lithofacies using logs labelled by rock cores. However, these methods have accuracy limits to some extent. To further improve their accuracies, practical and novel ensemble learning strategies and principles are proposed in this work, which allows geologists not familiar with ML to establish a good ML lithofacies identification model and help geologists familiar with ML further improve accuracy of lithofacies identification. The ensemble learning strategy combines ML methods as sub-classifiers to generate a comprehensive lithofacies identification model, which aims to reduce the variance errors in prediction. Each sub-classifier is trained by randomly sampled labelled data with random features. The novelty of this work lies in the ensemble principles making sub-classifiers just overfitting by algorithm parameter setting and sub-dataset sampling. The principles can lower the bias errors in the prediction. Two issues are discussed, videlicet (1) whether only a relatively simple single-classifier method can be as sub-classifiers and how to select proper ML methods as sub-classifiers; (2) whether different kinds of ML methods can be combined as sub-classifiers. If yes, how to determine a proper combination. In order to test the effectiveness of the ensemble strategy and principles for lithofacies identification, different kinds of machine learning algorithms are as sub-classifiers, including statistical classifiers (LDA, NB, KNN, ID3 tree and CART), kernel method (SVM), and ensemble learning algorithms (RF, AdaBoost, XGBoost and LightGBM). The experiments used a published dataset of lithofacies from Daniudi gas field (DGF) in Ordes Basin, China. Based on a series of comparisons between ML algorithms and their corresponding ensemble models using the ensemble strategy and principles, conclusions are drawn: (1) not only decision tree but also other single-classifiers and ensemble-learning-classifiers can be as sub-classifiers of homogeneous ensemble learning and obtain a higher accuracy; (2) the ensemble principles for the introduced homogeneous and heterogeneous ensemble strategy are effective to improve ML in lithofacies identification; (3) in practice, heterogeneous ensemble is more suitable for building a more powerful lithofacies identification model, though it is complex.

Assessment of the Propensity of Rocks of the Irtysh Deposit to Rock Impacts by Core Disking and by the Brittleness Coefficient

An assessment of the stress-strain state at deep (below horizon 14) of the Irtysh mine has been carried out. The propensity of ores and rocks of the Irtysh deposit to rock burst hazard is estimated: by disking of core and fragility of rocks. Studies of physical and mechanical properties were carried out at all stages of the development of the Irtysh deposit. In order to include in the diagram the levels of the impact potential, a sample was made for more than 136 definitions of the compressive and tensile strength of ores and rocks of the deposit

Measuring autoionization decay lifetimes of optically forbidden inner valence excited states in neon atoms with attosecond noncollinear four-wave-mixing spectroscopy

Attosecond noncollinear four wave mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48 eV XUV photon excites a 2s electron into the 2s2p6[np] Rydberg series, broadband NIR pulses couple the 2s2p6[3p] XUV-bright state to neighboring 2s2p6[3s] and 2s2p6[3d] XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or bright states, respectively. Experimental lifetimes for the 3s, 3p, and 3d states are measured to be 7 +/- 2 fs, 48 +/- 8 fs, and 427 +/- 40 fs, respectively, with 95% confidence. Accompanying calculations with two independent ab initio theoretical methods, NewStock and ASTRA, verify the findings. The results support the expected trend that the autoionization lifetime should be longer for states that have a smaller penetration in the radial region of the 2s core hole, which in this case is for the higher angular momentum Rydberg orbitals. The underlying theory thus links the lifetime results to electron correlation and provides an assessment of the direct and exchange terms in the autoionization process.

How pore pressure changes affect stress and strain in fault zones with complex internal structure – Insights from hydromechanical modelling

Faults not only affect the hydraulic regime and the local stress state, but are also prone to reactivation by pore pressure changes, potentially leading to induced seismicity, among others. In the present study, a generic finite element model with a detailed fault zone description including damage zones and a fault core with highly strained rock and fault core lenses of host rock is used to study the stress and strain evolution due to pore pressure changes. Special focus is on the temporal evolution of the effective stresses within the fault zone and the strain partitioning between its various subunits. The coupled hydromechanical simulations comprise five different scenarios covering pore pressure increase due to fluid injection and pore pressure decrease due to fluid production for permeable and semipermeable fault zones as well as different distances between the fault core lenses. Modelling results show that the variable hydromechanical properties of the different fault zone rocks lead to spatially and temporarily highly heterogeneous stress and strain patterns within the fault zone and its surrounding. In particular, substantial stress rotations of up to 45° and differently in the various subunits of the fault zone are found in response to pore pressure changes. Plastic straining as an indication for potential fault reactivation is observed particularly in the injection scenarios. Models provide a template for modifications with respect to fault zone architecture and hydromechanical properties. They can also serve as starting point to define bulk fault zone properties for reservoir-scale simulations which cannot capture the complexities of a fault zone regarding geometry and material distribution.

Grain boundary widening controls siderite (FeCO3) replacement of limestone (CaCO3)

The microstructure of minerals and rocks can significantly alter reaction rates. This study focuses on identifying transport paths in low porosity rocks based on the hypothesis that grain boundary widening accelerates reactions in which one mineral is replaced by another (replacement reaction). We conducted a time series of replacement experiments of three limestones (CaCO3) of different microstructures and solid impurity contents using FeCl2. Reacted solids were analyzed using chemical imaging, small angle X-ray and neutron scattering and Raman spectroscopy. In high porosity limestones replacement is reaction controlled and complete replacement was observed within 2 days. In low porosity limestones that contain 1–2% dolomite impurities and are dominated by grain boundaries, a reaction rim was observed whose width did not change with reaction time. Siderite (FeCO3) nucleation was observed in all parts of the rock cores indicating the percolation of the solution throughout the complete core. Dolomite impurities were identified to act as nucleation sites leading to growth of crystals that exert force on the CaCO3 grains. Widening of grain boundaries beyond what is expected based on dissolution and thermal grain expansion was observed in the low porosity marble containing dolomite impurities. This leads to a self-perpetuating cycle of grain boundary widening and reaction acceleration instead of reaction front propagation.

Chemostratigraphy and source of mercury in the Tropical Western Pacific over the past 600 kyr

To characterize the geochemical records of mercury (Hg) in the western tropical Pacific in the last 600 ka, the total concentration of Hg, and its isotopic compositions in Hole B at Site U1486 from the Western Pacific Warm Pool (WPWP) were determined. Some marked positive values of Δ199Hg in this core, and some Δ200Hg also exhibit significant positive, which resultes from the photoreduction of the volcanic Hg deposits through the long-range atmospheric transportation. In addition, dual odd-even Hg isotopes (Δ199Hg and Δ200Hg) database was also compiled to account for quantitative contributions to potential Hg sources, including marine Hg source, atmospheric Hg deposition, volcanic Hg source, and terrigenous Hg inputs. This study presents that sedimentary Hg in the core Hole B at Site U1486 originates mainly from the marine Hg source with a mean of 64.13%, which is similar to the changes of paleo-productivity in the WPWP with a character of the glacial-interglacial variation. The contributions of atmospheric Hg deposition, volcanic Hg source, and terrigenous Hg inputs represented approximately 17.88%, 10.37%, and 7.87% of the total Hg burden in this core, respectively. During the last 100 ka, the contribution of volcanic Hg source has increased overall, suggesting the increase of volcanic activity. And the amount of atmospheric Hg deposition in this core also generally increased during this period, which was in resonance with the eolian dust in the western Pacific. Furthermore, terrigenous Hg inputs in this study could be related to intensity of monsoon precipitation with an overall increasing trend. In this study, volcanic activities in sediment cores from the western Pacific can provide an additional and independent tool for the precise dating and synchronization of paleoenvironmental changes in these climatically significant regions.

Enumerating hydraulically active fractures using multiple, high-resolution datasets to inform plume transport in a sandstone aquifer

It is widely known that flow in fractured sedimentary rock is dominated by the interconnected fractures in the rock mass, but it is difficult to determine which fractures observed in boreholes are active, meaning they transmit water under natural gradient conditions A methodology is presented that uses optical televiewer (OTV) and continuous core logs synergistically with FLUTe™ Transmissivity (T) profiling, straddle packer testing, rock core permeability testing, active line source temperature logs, and rock core VOC concentration profiles to determine the number and position of active fractures in a 196-meter borehole in sandstone. The application of this methodology indicates that 40% of the identified fractures are active in this borehole with a frequency of 0.61 active fractures per meter, which compares well with the number of fractures identified with the straddle packer Rec method used in the largest transmissive zones, while the low transmissivity zones tested are consistent with laboratory-measured rock matrix hydraulic conductivity. High-resolution, hydraulically based methods provide the necessary evidence to improve estimates of active fractures that control solute transport. This paper demonstrates how multiple, spatially resolved data sets can be used synergistically to inform fracture network parameters thereby constraining hydraulic aperture and surface area calculations that control flow and diffusion, with the aim of improving the estimation of plume migration rates and mass discharge to receptors in fractured sedimentary rocks.

Slater transition methods for core-level electron binding energies.

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.

Strong configuration-interaction contributions to the angle-resolved 4p photoelectron spectra of atomic xenon

High-resolution photoelectron spectra of xenon (Xe) were measured in the $4p$ photoionization region. The anisotropy parameters \ensuremath{\beta} were obtained for several photoelectron peaks with angle-resolved photoelectron measurements. The various complicated spectral features were observed due to the perturbed $4{p}^{\ensuremath{-}1}$ spin-orbit doublet and adjacent satellite structures. An analysis based on a relativistic multiconfiguration calculation has been carried out. The key role of the strong interactions between the $4{p}^{\ensuremath{-}1}$ core hole and the $4{d}^{\ensuremath{-}2}nl$ configurations has been investigated in detail. Experimental peak energies and intensities are in good agreement with theory. We find that the many of the complicated features are $4{d}^{\ensuremath{-}2}nl$ satellite lines, and their intensities are determined mostly by the amount of $4{p}^{\ensuremath{-}1}$ configurations that are mixed in. The experimental \ensuremath{\beta} values agree quite well with theory, indicating that the photoelectron angular distributions are also strongly influenced by the $4p$ direct-ionization contributions.

Resonant inelastic x-ray scattering from U3O8 and UN

Resonant inelastic x-ray scattering (RIXS) using an incident energy tuned to the uranium absorption edges is reported from epitaxial films of α-U3O8 and UN. Theory shows that for U3O8 the multiplets associated with a 5f 1 configuration with a ground state of and the excited state of are observed. However, the strong transition predicted at a transfer energy of 1.67 eV is not observed. We assume this is a consequence of the intermediate state lifetime broadening due to interaction with continuum states when the transferred energy exceeds the onset of the continuum in the presence of the core hole. This hypothesis is supported by the results obtained for the 5f-itinerant system UN, where no sharp transitions have been observed, although the broad scattering response centred at ∼1 eV is considered a signature of a predominantly 5f 3 configuration in this band-like semi-metallic system. These experiments and theory add important information on these materials, both of which have been investigated since the 1960s, as well as whether RIXS at the uranium N edge can become a valuable tool for actinide research.

Upscaling Permeability Using Multiscale X‐Ray‐CT Images With Digital Rock Modeling and Deep Learning Techniques

AbstractThis study presents a workflow to predict the upscaled absolute permeability of the rock core direct from CT images whose resolution is not sufficient to allow direct pore‐scale permeability computation. This workflow exploits the deep learning technique with the data of raw CT images of rocks and their corresponding permeability value obtained by performing flow simulation on high‐resolution CT images. The permeability map of a much larger region in the rock core is predicted by the trained neural network. Finally, the upscaled permeability of the entire rock core is calculated by the Darcy flow solver, and the results showed a good agreement with the experiment data. This proposed deep learning based upscaling method allows estimating the permeability of large‐scale core samples while preserving the effects of fine‐scale pore structure variations due to the local heterogeneity.

Passive Wireless Pressure Gradient Measurement System for Fluid Flow Analysis

Using distributed MEMS pressure sensors to measure small flow rates in high resistance fluidic channels is fraught with challenges far beyond the performance of the pressure sensing element. In a typical core-flood experiment, which may last several months, flow-induced pressure gradients are generated in porous rock core samples wrapped in a polymer sheath. Measuring these pressure gradients along the flow path requires high resolution pressure measurement while contending with difficult test conditions such as large bias pressures (up to 20 bar) and temperatures (up to 125 °C), as well as the presence of corrosive fluids. This work is directed at a system for using passive wireless inductive-capacitive (LC) pressure sensors that are distributed along the flow path to measure the pressure gradient. The sensors are wirelessly interrogated with readout electronics placed exterior to the polymer sheath for continuous monitoring of experiments. Using microfabricated pressure sensors that are smaller than ø15 × 3.0 mm3, an LC sensor design model for minimizing pressure resolution, accounting for sensor packaging and environmental artifacts is investigated and experimentally validated. A test setup, built to provide fluid-flow pressure differentials to LC sensors with conditions that mimic placement of the sensors within the wall of the sheath, is used to test the system. Experimental results show the microsystem operating over full-scale pressure range of 20,700 mbar and temperatures up to 125 °C, while achieving pressure resolution of <1 mbar, and resolving gradients of 10-30 mL/min, which are typical in core-flood experiments.

Tectono-sedimentary characteristics and controlling factors of the lower-middle Cambrian gypsum-salt rocks in the Tarim Basin, Northwest China

Due to their excellent sealing capacity, gypsum-salt rocks are often associated with hydrocarbon accumulations. In the Tarim Basin (Northwest China), exploration activity has demonstrated that the Cambrian gypsum-salt rocks played a key role in the development of hydrocarbon plays, but there is still a lack of research on them. This study utilizes geological data coming from outcrops, well logs, rock cores, and seismic reflection profiles to quantify the distribution and tectono-sedimentary characteristics of the Cambrian gypsum-salt rocks in the Tarim Basin, and decipher the controlling factors governing their deposition. The gypsum-salt rocks are present in the Lower Cambrian Wusonger and the Middle Cambrian Awatage Formations, which are distributed around the Aman and Awati depressions, two structures inherited from the Ediacaran intracontinental rift, and the Bachu uplift. These Formations are mainly composed of salt, gypsum, gypsum halite, gypsum dolomite and gypsum mudstone, and are usually deposited in medium-thin beds. The total and single layer thicknesses of gypsum-salt rocks in the north of Bachu uplift are greater than that in the south. These lithofacies can be associated with different environments of deposition, with the Bachu uplift interpreted as supratidal sabkhas and evaporation lagoons and the Aman-Awati depressions as large-scale evaporation salt basins with a bull's eye architecture of halite-gypsum-dolomite. Carbon and oxygen isotopes indicate an overall fall in relative sea level from the late Early Cambrian to the Middle Cambrian in the Tarim Basin, accompanied by higher-frequency oscillations. Influenced by this continuous decline of sea level, the eastern platform margin transformed from gentle ramp to progradational rimmed margin and blocked the water exchange between the open sea and the platform. The southwest side of the platform was characterized by a stable gentle ramp margin, which was flooded by seawater during rise of sea level. In addition, the development of the intraplatform shoals further provided morphological barriers for the lagoons in the Bachu-Tazhong uplift belt. The Aman-Awati depressions continued to subside during the Early and Middle Cambrian and became the main loci of salt deposition, whereas the depressions and half grabens formed under the tensile tectonic regime in the Bachu-Tazhong uplift belt controlled the development of evaporation lagoons and gypsum-salt flats. This study constrained the distribution and evolution of gypsum-salt caprocks, and thus provide new insights for the sub-salt and inter-salt hydrocarbon exploration in the Tarim Basin.

Sedimentary Microfacies and Sand Body Characteristics at Segment 2 of the Sangonghe Formation in Oilfield A on the South Slope District of the Mahu Depression

The South Slope District of the Mahu Depression in the Junggar Basin, a major favorable zone for middle and superficial oil–gas exploration, has experienced industrial gas flow. However, research on the sedimentary microfacies characteristics of Segment 2 of the Sangonghe Formation, the main oil-bearing formation, remains lacking. In this study, the rock type, sedimentary tectonics, and sedimentary microfacies of Segment 2 of the Jurassic Sangonghe Formation in the South Slope District of the Mahu Depression were thoroughly investigated through 3D seismic, rock core, and logging data. Moreover, the sedimentary modes and distribution characteristics of the sand bodies in the study area were further analyzed. Results showed that subfacies at the front edge of the braided river delta are developed at Segment 2 of the Sangonghe Formation, which can be further divided into four microfacies types, namely, underwater distributary channel, sheet sand, estuary dam, and interdistributary bay. The estuary dam is only developed at local positions in the work area. The vertical evolutionary laws from Segment 2 of the Sangonghe Formation to Segment 3 of the Sangonghe Formation are explicit and manifest as retrogradation from the subfacies at the front edge of the braided river delta to the prodelta. The sand bodies formed by frequent swings of the underwater distributary channels are the main reservoir bodies, and the lithology is mainly fine-grained feldspar lithic sandstone, and sedimentary tectonics have diverse forms. On the basis of deposition microphase analysis, the sand bodies’ planar distribution characteristics under phase-controlled conditions were analyzed using a seismic model inversion technology to provide theoretical guidance for oilfield expansion, exploration, and exploitation.

Constraints on the thermal evolution of metamorphic core complexes from the timing of high-pressure metamorphism on Naxos, Greece

Metamorphic core complexes are classically interpreted to have formed during crustal extension, although many also occur in compressional environments. New U−(Th)−Pb allanite and xenotime geochronologic data from the structurally highest Zas Unit (Cycladic Blueschist Unit) of the Naxos metamorphic core complex, Greece, integrated with pressure−temperature−time (P−T−t) histories, are incorporated into a thermal model to test the role of crustal thickening and extension in forming metamorphic core complexes. Metamorphism on Naxos is diachronous, with peak metamorphic conditions propagating down structural section over a ∼30−35 m.y. period, from ca. 50 Ma to 15 Ma. At the highest structural level, the Zas Unit records blueschist-facies metamorphism (∼14.5−19 kbar, 470−570 °C) at ca. 50 Ma, during northeast-directed subduction of the Adriatic continental margin. The Zas Unit was subsequently extruded toward the SW and thrust over more proximal continental margin and basement rocks (Koronos and Core units). This contractional episode resulted in crustal thickening and Barrovian metamorphism from ca. 40 Ma and reached peak kyanite-sillimanite−grade conditions of ∼10−5 kbar and 600−730 °C at 20−15 Ma. Model P−T−t paths, assuming conductive relaxation of isotherms following overthrusting, are consistent with the clockwise P−T−t evolution. In contrast, extension results in exhumation and cooling of the crust, which is inconsistent with key components of the thermal evolution. Barrovian metamorphism on Naxos is therefore interpreted to have resulted from crustal thickening over a ∼30−35 m.y. time period prior to extension, normal faulting, and rapid exhumation after a thermal climax at ca. 15 Ma.

Research on Adaptability Evaluation Method of Polymer by Nuclear Magnetic Resonance Technology.

In order to study the matching relationship between polymer(HPAM) molecular weight and reservoir permeability, in this paper, the injection performance of polymers with different molecular weights in rock cores with different permeability is studied. Using nuclear magnetic resonance technology combined with conventional core displacement equipment, the change law of the displacement process was analyzed from three aspects of nuclear magnetic resonance T2 spectrum, core layering, and imaging. Finally, the fluidity of the polymer solution in the core was analyzed by injection pressure control features. The experimental results show that the polymer solution with a molecular weight of 25 million has the best retention effect in the core flooding experiment and can stay in the dominant channel of the core for a long time to control the water flooding mobility. In rocks with a permeability of 500, 1000, and 2000 mD, subsequent water flooding can expand the swept volume by about 25% compared with polymer flooding. This method can effectively establish the adaptability matching relationship between the polymer molecular weight and the reservoir permeability.

The core ionization energies calculated by delta SCF and Slater's transition state theory.

The core ionization energies of the second-period and third-period elements are studied by ΔSCF and Slater's transition state (STS) theory by using Hartree-Fock (HF) and Kohn-Sham (KS) approximations. Electron correlation increases the estimated core ionization energies, while the self-interaction error (SIE) decreases them, especially for the third-period elements and is a more significant factor. As a result, while HF lacks electron correlation, it is free of SIE and reasonably predicts the core ionization energies. The core ionization energies calculated by HF STS are very close to those calculated by HF ΔSCF, showing that STS reasonably describes the relaxation of the core hole. The core ionization energies calculated by KS are particularly sensitive to the SIE of the functional used, with functionals having less SIE yielding more accurate ΔSCF core ionization energies. Consequently, BH&HLYP gives better results than B3LYP and LC-BOP since BH&HLYP is the hybrid functional with high proportion of the exact HF exchange. Although the core ionization energies are underestimated by ΔSCF due to SIE, STS gives larger core ionization energies than ΔSCF due to a concave behavior of the error curves of STS, which is also related to SIE. The mean absolute deviations of STS relative to ΔSCF, and relative to the experiment, are almost constant regardless of the nuclei among the element in the second period, and likewise among those in the third period. The systematic nature suggests that shifting the STS core ionization energies may be useful. We propose the shifted STS (1) for reproducing ΔSCF values, and the shifted STS (2) to reproduce the observed ones for KS calculations. Both schemes work quite well. The calculated results of KS ΔSCF and STS vary depending on the functional. However, the variation of each species' shifted STS (2) is very small, and all shifted STS (2) values are close to the observed ones. As the shifted STS require only one SCF calculation, they are simple and practical for predicting the core ionization energies.