Abstract: We introduce a machine learning method in which energy solutions from the Schrodinger equation are predicted using symmetry adapted atomic orbital features and a graph neural-network architecture. OrbNet is shown to outperform existing methods in terms of learning efficiency and transferability for the prediction of density functional theory results while employing low-cost features that are obtained from semi-empirical electronic structure calculations. For applications to datasets of drug-like molecules, including QM7b-T, QM9, GDB-13-T, DrugBank, and the conformer benchmark dataset of Folmsbee and Hutchison [Int. J. Quantum Chem. (published online) (2020)], OrbNet predicts energies within chemical accuracy of density functional theory at a computational cost that is 1000-fold or more reduced.

Abstract: The BDF (Beijing Density Functional) program package is in the first place a platform for theoretical and methodological developments, standing out particularly in relativistic quantum chemical methods for chemistry and physics of atoms, molecules, and periodic solids containing heavy elements. These include the whole spectrum of relativistic Hamiltonians and their combinations with density functional theory for the electronic structure of ground states as well as time-dependent and static density functional linear response theories for electronically excited states and electric/magnetic properties. However, not to be confused by its name, BDF nowadays comprises also of standard and novel wave function-based correlation methods for the ground and excited states of strongly correlated systems of electrons [e.g., multireference configuration interaction, static-dynamic-static configuration interaction, static-dynamic-static second-order perturbation theory, n-electron valence second-order perturbation theory, iterative configuration interaction (iCI), iCI with selection plus PT2, and equation-of-motion coupled-cluster]. Additional features of BDF include a maximum occupation method for finding excited states of Hartree-Fock/Kohn-Sham (HF/KS) equations, a very efficient localization of HF/KS and complete active space self-consistent field orbitals, and a unique solver for exterior and interior roots of large matrix eigenvalue problems.

Abstract: Layered kagome-lattice 3d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands with bandwidth less than 0.2 eV run through the whole Brillouin zone, especially the bandwidth of the flat band of out-of-plane orbitals is less than 0.02 eV along G-M. The energy gap induced by spin-orbit interaction at the Dirac cone of out-of-plane orbitals is much smaller than that of in-plane orbitals, suggesting orbital-selective character of the Dirac fermions.

Abstract: The reversible control of a single spin of an atom or a molecule is of great interest in Kondo physics and a potential application in spin based electronics.Here we demonstrate that the Kondo resonance of manganese phthalocyanine molecules on an Au(111) substrate have been reversibly switched off and on via a robust route through attachment and detachment of single hydrogen atom to the magnetic core of the molecule. As further revealed by density functional theory calculations, even though the total number of electrons of the Mn ion remains almost the same in the process, gaining one single hydrogen atom leads to redistribution of charges within 3d orbitals with a reduction of the molecular spin state from S = 3/2 to S = 1 that directly contributes to the Kondo resonance disappearance. This process is reversed by a local voltage pulse or thermal annealing to desorb the hydrogen atom.

Abstract: We report the transition metal quantum mechanics (tmQM) data set, which contains the geometries and properties of a large transition metal-organic compound space. tmQM comprises 86,665 mononuclear complexes extracted from the Cambridge Structural Database, including Werner, bioinorganic, and organometallic complexes based on a large variety of organic ligands and 30 transition metals (the 3d, 4d, and 5d from groups 3 to 12). All complexes are closed-shell, with a formal charge in the range {+1, 0, -1}e. The tmQM data set provides the Cartesian coordinates of all metal complexes optimized at the GFN2-xTB level, and their molecular size, stoichiometry, and metal node degree. The quantum properties were computed at the DFT(TPSSh-D3BJ/def2-SVP) level and include the electronic and dispersion energies, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, HOMO/LUMO gap, dipole moment, and natural charge of the metal center; GFN2-xTB polarizabilities are also provided. Pairwise representations showed the low correlation between these properties, providing nearly continuous maps with unusual regions of the chemical space, for example, complexes combining large polarizabilities with wide HOMO/LUMO gaps and complexes combining low-energy HOMO orbitals with electron-rich metal centers. The tmQM data set can be exploited in the data-driven discovery of new metal complexes, including predictive models based on machine learning. These models may have a strong impact on the fields in which transition metal chemistry plays a key role, for example, catalysis, organic synthesis, and materials science. tmQM is an open data set that can be downloaded free of charge from https://github.com/bbskjelstad/tmqm.

Abstract: The origins of the complex Fe 2p X-Ray Photoelectron Spectra (XPS) of hematite (α-Fe2O3) are analyzed and related to the character of the bonding in this compound. This analysis provides a new and novel view of the reasons for XPS binding energies (BEs) and BE shifts, which deepens the current understanding and interpretation of the physical and chemical significance of the XPS. In particular, many-body effects are considered for the initial and the final, 2p-hole configuration wavefunctions. It is shown that a one-body or one-configuration analysis is not sufficient and that the many-body, many-determinantal, and many-configurational character of the wavefunctions must be taken into account to describe and understand why the XPS intensity is spread over an extremely large number of final 2p-hole multiplets. The focus is on the consequences of angular momentum coupling of the core and valence open shell electrons, the ligand field splittings of the valence shell orbitals, and the degree of covalent mixing of the Fe(3d) electrons with the O(2p) electrons. Novel theoretical methods are used to estimate the importance of these various terms. An important consequence of covalency is a reduction in the energy separation of the multiplets. Although shake satellites are not considered explicitly, the total losses of intensity from the angular momentum multiplets to shake satellites is determined and related to the covalent character of the Fe-O interaction. The losses are found to be the same for Fe 2p1/2 and 2p3/2 ionization.

Abstract: Tuning the energies of molecular excited states is a central research theme in modern chemistry with high relevance for optoelectronic applications and chemical synthesis. Whereas frontier orbitals have proven to be an intuitive and simple model in many cases, they can only provide a very rough approximation of the underlying wavefunctions. The purpose of this Perspective is to explore how our qualitative understanding of electronic excitation processes can be promoted beyond the molecular orbital picture by exploiting methods and insights from modern quantum chemistry. For this purpose, the physics of a correlated electron–hole pair is analysed in detail to show the origin of exchange repulsion and a dynamic Coulomb attraction, which determine its energy aside from the orbital energies. Furthermore, we identify and discuss the two additional effects of secondary orbital relaxation and de-excitations. Rules for reconstructing these four contributions from general excited-state computations are presented and their use is exemplified in three case studies concerned with the relative ordering of the singlet and triplet ππ* and nπ* states of uracil, the large energetic differences between the first singlet and triplet states of the polyacenes, and the assignment of plasmonic states in octatetraene. Finally, we lay out some general ideas for how the knowledge gained could ultimately lead to new design principles for tuning molecular excitation energies as well as for diagnosing possible shortcomings of commonly used electronic structure methods.

Abstract: Quantum dot-like single-photon sources in transition metal dichalcogenides (TMDs) exhibit appealing quantum optical properties but lack a well-defined atomic structure and are subject to large spectral variability. Here, we demonstrate electrically stimulated photon emission from individual atomic defects in monolayer WS2 and directly correlate the emission with the local atomic and electronic structure. Radiative transitions are locally excited by sequential inelastic electron tunneling from a metallic tip into selected discrete defect states in the WS2 bandgap. Coupling to the optical far field is mediated by tip plasmons, which transduce the excess energy into a single photon. The applied tip-sample voltage determines the transition energy. Atomically resolved emission maps of individual point defects closely resemble electronic defect orbitals, the final states of the optical transitions. Inelastic charge carrier injection into localized defect states of two-dimensional materials provides a powerful platform for electrically driven, broadly tunable, atomic-scale single-photon sources.

Abstract: We introduce a machine learning method in which energy solutions from the Schrodinger equation are predicted using symmetry adapted atomic orbitals features and a graph neural-network architecture. \textsc{OrbNet} is shown to outperform existing methods in terms of learning efficiency and transferability for the prediction of density functional theory results while employing low-cost features that are obtained from semi-empirical electronic structure calculations. For applications to datasets of drug-like molecules, including QM7b-T, QM9, GDB-13-T, DrugBank, and the conformer benchmark dataset of Folmsbee and Hutchison, \textsc{OrbNet} predicts energies within chemical accuracy of DFT at a computational cost that is thousand-fold or more reduced.

Abstract: Photoionization is one of the fundamental light-matter interaction processes in which the absorption of a photon launches the escape of an electron. The time scale of the process poses many open questions. Experiments found time delays in the attosecond ($10^{-18}$ s) domain between electron ejection from different orbitals, electronic bands, or in different directions. Here, we demonstrate that across a molecular orbital the electron is not launched at the same time. The birth time rather depends on the travel time of the photon across the molecule, which is 247 zeptoseconds ($10^{-21}$ s) for the average bond length of H$_2$. Using an electron interferometric technique, we resolve this birth time delay between electron emission from the two centers of the hydrogen molecule.

Abstract: The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts to answer this question have, among other methods, given rise to semi-empirical quantum chemistry in minimal basis representation. We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [K. T. Schutt et al., Nat. Commun. 10, 5024 (2019)] for electronic wave functions in an optimized quasi-atomic minimal basis representation. For five organic molecules ranging from 5 to 13 heavy atoms, the model accurately predicts molecular orbital energies and wave functions and provides access to derived properties for chemical bonding analysis. Particularly for larger molecules, the model outperforms the original atomic-orbital-based SchNOrb method in terms of accuracy and scaling. We conclude by discussing the future potential of this approach in quantum chemical workflows.

Abstract: We construct a family of translationally invariant lattice models with a large number ($N$) of orbitals at every site coupled together via single electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, that have a modified Sachdev-Ye-Kitaev (SYK) form, we demonstrate a number of unusual features at strong coupling and in the large$-N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi liquid metal, and, (ii) an instability of an incipient heavy Fermi liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong-coupling, these solvable models display pairing instabilities that are not driven by any special "nesting" properties associated with an underlying Fermi surface.

Abstract: In the Noisy Intermediate-Scale Quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the "killer application" for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While physically motivated, this approximation can severely impact the description of these complicated features. A perfect example is that of conical intersections (i.e. a singular point of degeneracy between electronic states), which are of primary importance to understand many prominent reactions. Designing active spaces so that the improved accuracy from a quantum computer is not rendered useless is key to finding useful applications of these promising devices within the field of chemistry. To answer this issue, we introduce a NISQ-friendly method called "State-Averaged Orbital-Optimized Variational Quantum Eigensolver" (SA-OO-VQE) which combines two algorithms: (1) a state-averaged orbital-optimizer, and (2) a state-averaged VQE. To demonstrate the success of the method, we classically simulate it on a minimal Schiff base model (namely the formaldimine molecule CH2NH) relevant also for the photoisomerization in rhodopsin -- a crucial step in the process of vision mediated by the presence of a conical intersection. We show that merging both algorithms fulfil the necessary condition to describe the molecule's conical intersection, i.e. the ability to treat degenerate (or quasi-degenerate) states on the same footing.

Abstract: Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates the strong spin-orbit effect of the single-atomic impurity at the quantum level, suggesting that a nonmagnetic impurity can introduce spin-orbit coupled magnetic resonance in topological magnets.

Abstract: We propose a scheme for the construction of the one-particle Green's function (GF) of an interacting electronic system via statistical sampling on a quantum computer. Although the nonunitarity of creation and annihilation operators for the electronic spin orbitals prevents us from preparing specific states selectively, probabilistic state preparation is demonstrated to be possible for the qubits. We provide quantum circuits equipped with at most two ancillary qubits for obtaining all the components of the GF. We perform simulations of such construction of GFs for LiH and ${\mathrm{H}}_{2}\mathrm{O}$ molecules based on the unitary coupled-cluster (UCC) method to demonstrate the validity of our scheme by comparing the quasiparticle and satellite spectra exact within the UCC method and those from full configuration-interaction calculations. We also examine the accuracy of the sampling method by exploiting the Galitskii-Migdal formula, which gives the total energy only from the GF.

Abstract: We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Moller-Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of [Formula: see text], our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.

Abstract: The recent and exciting discovery of superconductivity in the hole-doped infinite-layer nickelate Nd 1-{\delta} Sr {\delta} NiO 2 draws strong attention to correlated quantum materials. From a theoretical view point, this new class of unconventional superconducting materials provides an opportunity to unveil new physics in correlated quantum materials. Here we study the temperature and doping dependence of the local spectrum as well as the charge, spin and orbital susceptibilities from first principles. By using ab initio LQSGW+DMFT methodology, we show that onsite Hund's coupling in Ni-d orbitals gives rise to multiple signatures of Hund's metallic phase in Ni-eg orbitals. The proposed picture of the nickelates as an eg (two orbital) Hund's metal differs from the picture of the Fe-based superconductors as a five orbital Hund's metal as well as the picture of the cuprates as doped charge transfer insulators. Our finding unveils a new class of the Hunds metals and has potential implications for the broad range of correlated two orbital systems away from half-filling.

Abstract: Frontier orbitals, i.e., the highest occupied and lowest unoccupied orbitals of a molecule, generally determine molecular properties, such as chemical bonding and reactivities. Consequently, there has been a lot of interest in measuring them, despite the fact that, strictly speaking, they are not quantum-mechanical observables. Yet, with photoemission tomography a powerful technique has recently been introduced by which the electron distribution in orbitals of molecules adsorbed at surfaces can be imaged in momentum space. This has even been used for the identification of reaction intermediates in surface reactions. However, so far it has been impossible to follow an orbital's momentum-space dynamics in time, for example through an excitation process or a chemical reaction. Here, we report a key step in this direction: we combine time-resolved photoemission employing high laser harmonics and a recently developed momentum microscope to establish a tomographic, femtosecond pump-probe experiment of unoccupied molecular orbitals. Specifically, we measure the full momentum-space distribution of transiently excited electrons. Because in molecules this momentum-space distribution is closely linked to orbital shapes, our experiment offers the extraordinary possibility to observe ultrafast electron motion in time and space. This enables us to connect their excited states dynamics to specific real-space excitation pathways.

Abstract: Relativistic multireference ab initio wave function calculations with the restricted active space second-order perturbation theory (RASPT2) were performed on thorocene and uranocene to determine the actinide N4,5 -edge and carbon K-edge X-ray absorption near-edge structure (XANES) intensities and the metal-ligand orbital mixing in the ground state and core-excited states. Calculated spectral intensities show very good agreement with the experiments and therefore allow detailed and unambiguous assignment of the observed spectral features. φ-type covalent bonding or antibonding interactions are observed for thorocene in the core-excited states, though not in the ground state. This is because the molecular orbital of φ symmetry, which is the in-phase combination of the ligand Lφ and the Th 5fφ orbitals, can be populated with electrons in core-excited states, whereas it is essentially unoccupied in the ground state. For uranocene, the XANES spectra do not reveal much information beyond multiplet broadening, despite the presence of distinct peaks in the spectra. Every core-excited peak is best characterized by its own set of bond orbitals, as the excited state covalency is clearly different from the ground state covalency.

Abstract: Calculation of dynamical parameters for photoionization requires an accurate description of the initial and final states of the system, as well as of the outgoing electron. We show that using a linear combination of atomic orbitals B-spline density functional theory (DFT) method to describe the outgoing electron, in combination with correlated equation of motion coupled cluster singles and double Dyson orbitals, gives good agreement with experiment and outperforms other simpler approaches, like plane and Coulomb waves, used to describe the photoelectron. Results are presented for cross-sections, angular distributions, and dichroic parameters in chiral molecules, as well as for photoionization from excited states. We also present a comparison with the results obtained using Hartree-Fock and DFT molecular orbitals selected according to Koopmans' theorem for the bound states.

Abstract: The electronic structure of benzene is a battleground for competing viewpoints of electronic structure, with valence bond theory localising electrons within superimposed resonance structures, and molecular orbital theory describing delocalised electrons. But, the interpretation of electronic structure in terms of orbitals ignores that the wavefunction is anti-symmetric upon interchange of like-spins. Furthermore, molecular orbitals do not provide an intuitive description of electron correlation. Here we show that the 126-dimensional electronic wavefunction of benzene can be partitioned into tiles related by permutation of like-spins. Employing correlated wavefunctions, these tiles are projected onto the three dimensions of each electron to reveal the superposition of Kekule structures. But, opposing spins favour the occupancy of alternate Kekule structures. This result succinctly describes the principal effect of electron correlation in benzene and underlines that electrons will not be spatially paired when it is energetically advantageous to avoid one another. The electronic structure of benzene has been a test bed for competing theories along the years. Here the authors show via quantum chemistry calculations that the wavefunction of benzene can be partitioned into tiles which show that the two electron spins exhibit staggered Kekule structures.

Abstract: Electron and charge transfers are part of many vital processes in nature and technology. Ab initio descriptions of these processes provide useful insights that can be utilized for applications. A combination of the embedded cluster material model and nonorthogonal configuration interaction (NOCI), in which the cluster wave functions are expanded in many-electron basis functions (MEBFs) consisting of spin-adapted, antisymmetrized products of multiconfigurational wave functions of fragments (which are usually molecules) in the cluster, appears to provide a compromise between accuracy and calculation time. Additional advantages of this NOCI-Fragments approach are the chemically convenient interpretation of the wave function in terms of molecular states, and the direct accessibility of electronic coupling between diabatic states to describe energy and electron transfer processes. Bottlenecks in this method are the large number of two-electron integrals that have to be handled for the calculation of an electronic coupling matrix element and the enormous number of matrix elements over determinant pairs that have to be evaluated for the calculation of one matrix element between the MEBFs. We show here how we created a reduced common molecular orbital basis that is utilized to significantly reduce the number of two-electron integrals that need to be handled. The results obtained with this basis do not show any loss of accuracy in relevant quantities like electronic couplings and vertical excitation energies. We also show a significant reduction in computation time without loss in accuracy when matrix elements over determinant pairs with small weights are neglected in the NOCI. These improvements in the methodology render NOCI-Fragments to be also applicable to treat clusters of larger molecular systems with larger atomic basis sets and larger active spaces, as the computation time becomes dependent on the number of occupied orbitals and less dependent on the size of the active space.

Abstract: Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave amplitudes decay rapidly away from an isolated atomic core. This kind of description is essential in condensed-matter physics, and it rules the electronic transport properties of metals, insulators and many other solid-state systems. The corresponding phenomenology is well captured by tight-binding models, where the electronic band structure emerges from atomic orbitals of isolated atoms plus their coupling to neighboring sites in a crystal. In this work, a mechanical system that emulates dynamically a quantum tightly bound electron is built. This is done by connecting mechanical resonators via locally periodic aluminum bars acting as couplers. When the frequency of a particular resonator lies within the frequency gap of a coupler, the vibrational wave amplitude imitates a bound electron orbital. The localization of the wave at the resonator site and its exponential decay along the coupler are experimentally verified. The quantum dynamical tight-binding model and frequency measurements in mechanical structures show an excellent agreement. Some applications in atomic and condensed matter physics are suggested.

Abstract: AlGaN has attracted considerable interest for ultraviolet (UV) applications With the development of UV optoelectronic devices, abnormal carrier confinement behaviour has been observed for c-plane-oriented AlGaN quantum wells (QWs) with high Al content Because of the dispersive crystal field split-off hole band (CH band) composed of pz orbitals, the abnormal confinement becomes the limiting factor for efficient UV light emission This observation differs from the widely accepted concept that confinement of carriers at the lowest quantum level is more pronounced than that at higher quantum levels, which has been an established conclusion for conventional continuous potential wells In particular, orientational pz orbitals are sensitive to the confinement direction in line with the conducting direction, which affects the orbital intercoupling In this work, models of Al075Ga025N/AlN QWs constructed with variable lattice orientations were used to investigate the orbital intercoupling among atoms between the well and barrier regions Orbital engineering of QWs was implemented by changing the orbital state confinement, with the well plane inclined from 0° to 90° at a step of 30° (referred to the c plane) The barrier potential and transition rate at the band edge were enhanced through this orbital engineering The concept of orbital engineering was also demonstrated through the construction of inclined QW planes on semi- and nonpolar planes implemented in microrods with pyramid-shaped tops The higher emission intensity from the QWs on the nonpolar plane compared with those on the polar plane was confirmed via localized cathodoluminescence (CL) maps

Abstract: Machine learning methods have enabled the low-cost evaluation of molecular properties such as energy at an unprecedented scale. While many of such applications have focused on molecular input based on geometry, few studies consider representations based on the underlying electronic structure. Directing the attention to the electronic structure offers a unique challenge that allows for a more detailed representation of the underlying physics and how they affect molecular properties. The target of this work is to efficiently encode a lower-cost correlated wave function derived from MP2 to predict a higher-cost coupled-cluster singles-and-doubles (CCSD) wave function based on correlation-pair energies and the contributing electron promotions (excitations) and integrals. The new molecular representation explores the short-range behavior of electron correlation and utilizes distinct models that differentiate between two-electron promotions from the same molecular orbital or from two different orbitals. We present a re-engineered set of input features that provide an intuitive description of the orbital properties involved in electron correlation. The overall models are found to be highly transferable and size extensive, necessitating very few training instances to approach the chemical accuracy of a broad spectrum of organic molecules. The efficiency and transferability of the novel representation are demonstrated on a series of linear hydrocarbons, the potential energy surface of the water dimer, and on the GDB-9 database. For the GDB-9 database, we found that data from only 140 randomly selected molecules are adequate to achieve chemical accuracy for more than 133 000 organic molecules.

Abstract: We present an implementation of equation-of-motion oscillator strengths for the multilevel CCSD (MLCCSD) model where CCS is used as the lower level method (CCS/CCSD). In this model, the double excitations of the cluster operator are restricted to an active orbital space, whereas the single excitations are unrestricted. Calculated nitrogen K-edge spectra of adenosine, adenosine triphosphate (ATP), and an ATP-water system are used to demonstrate the performance of the model. Projected atomic orbitals (PAOs) are used to partition the virtual space into active and inactive orbital sets. Cholesky decomposition of the Hartree-Fock density is used to partition the occupied orbitals. This Cholesky-PAO partitioning is cheap, scaling as O(N3), and is suitable for the calculation of core excitations, which are localized in character. By restricting the single excitations of the cluster operator to the active space, as well as the double excitations, the CCSD-in-HF model is obtained. A comparison of the two models-MLCCSD and CCSD-in-HF-is presented for the core excitation spectra of the adenosine and ATP systems.