Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Iron pnictides as a new setting for quantum criticality

Two major themes in the physics of condensed matter are quantum critical phenomena and unconventional superconductivity. These usually occur in the context of competing interactions in systems of strongly correlated electrons. All this interesting physics comes together in the behavior of the recently discovered iron pnictide compounds that have generated enormous interest because of their moderately high-temperature superconductivity. The ubiquity of antiferromagnetic ordering in their phase diagrams naturally raises the question of the relevance of magnetic quantum criticality, but the answer remains uncertain both theoretically and experimentally. Here, we show that the undoped iron pnictides feature a unique type of magnetic quantum critical point, which results from a competition between electronic localization and itinerancy. Our theory provides a mechanism to understand the experimentally observed variation of the ordered moment among the undoped iron pnictides. We suggest P substitution for As in the undoped iron pnictides as a means to access this example of magnetic quantum criticality in an unmasked fashion. Our findings point to the iron pnictides as a much-needed setting for quantum criticality, one that offers a unique set of control parameters.

Multidimensional attosecond resonant X-ray spectroscopy of molecules: lessons from the optical regime

New free-electron laser and high-harmonic generation X-ray light sources are capable of supplying pulses short and intense enough to perform resonant nonlinear time-resolved experiments in molecules. Valence-electron motions can be triggered impulsively by core excitations and monitored with high temporal and spatial resolution. We discuss possible experiments that employ attosecond X-ray pulses to probe the quantum coherence and correlations of valence electrons and holes, rather than the charge density alone, building on the analogy with existing studies of vibrational motions using femtosecond techniques in the visible regime.

Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation?

The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.

Conceptual Insights into DFT Spin-State Energetics of Octahedral Transition-Metal Complexes through a Density Difference Analysis

In this study, an intuitive concept is derived, which explains the characteristic dependence of spin-state energetics on the exact exchange admixture of DFT functionals in the case of octahedral transition metal complexes. The change in electron density distributions upon varying the admixture, c₃ , in the B3LYP functional is analyzed for archetype ionic and covalent systems as well as for the Fe²⁺ ion in an ideal octahedral field. An understanding of how the DFT description of the electronic structure of octahedral complexes changes as a function of c₃ is sought. A systematic spin-state energy analysis of 50 octahedral complexes of various metals and ligands with consistent experimental data is presented, allowing the derivation, in theory, of an optimal c₃ value for each system. The notion that the admixture dependence of DFT spin-state energetics stems from the treatment of nondynamic electrons arising from the mixing of (M-Lz2 )⁰ (dz2 )² and (M-Lx2-y2 )⁰ (dx2-y2 )² configurations into the dominant (M-Lx2-y2 )² (dx2-y2 )⁰ and (M-Lx2-y2 )² (dx2-y2 )⁰ ones in the low(er) spin states is put forward. That is, in the effort to mimic such electron-electron interactions, E_x^LDA overestimates, whereas exact exchange downplays the contribution of this type of electron correlation to the stability of low(er) spin states, leading to the widespread practical observation that the higher the exact exchange admixture, the more stable the high-spin-state configuration.

Electrostatic Domination of the Effect of Electron Correlation in Intermolecular Interactions

The electron-electron correlation energy is negative, and attractive dispersion interactions are entirely a correlation effect; therefore, the contribution of correlation to intermolecular binding is commonly assumed to be negative, or binding in nature. However, there are many cases where the long-range correlation binding energy is positive, with certain geometries of the water dimer as a prominent example. Geometries with dipoles misaligned can also have an electrostatically dominated, though negative, long-range correlation binding. In either case, the interaction decays as R(-3). This has its origin in the systematic overestimation of dipole moments by Hartree-Fock theory, leading to a reduction in the calculated electrostatic attraction upon inclusion of correlation. Thus, energy decomposition analyses that include correlation but do not correct mean field electrostatic terms are suboptimal. Attenuated second-order Møller-Plesset theory, which smoothly truncates long-range electron correlation effects to zero, can, paradoxically, have the correct long-range behavior for many intermolecular interactions.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)₂] and dicyanomercury(II) [Hg(CN)₂]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)₂ and Hg(CN)₂, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

Electron Transport in Carbon Nanotubes with Adsorbed Chromium Impurities

We employ Green’s function method for describing multiband models with magnetic impurities and apply the formalism to the problem of chromium impurities adsorbed onto a carbon nanotube. Density functional theory is used to determine the bandstructure, which is then fit to a tight-binding model to allow for the subsequent Green’s function description. Electron–electron interactions, electron–phonon coupling, and disorder scattering are all taken into account (perturbatively) with a theory that involves a cluster extension of the coherent potential approximation. We show how increasing the cluster size produces more accurate results and how the final calculations converge as a function of the cluster size. We examine the spin-polarized electrical current on the nanotube generated by the magnetic impurities adsorbed onto the nanotube surface. The spin polarization increases with both increasing concentration of chromium impurities and with increasing magnetic field. Its origin arises from the strong electron correlations generated by the Cr impurities.

Polycyclic Hydrocarbons from [4n]Annulenes: Correlation versus Hybridization Forces in the Formation of Diradicaloids

The conceptual connections between [4n] Hückel antiaromaticity, disjoint orbitals, correlation energy, pro-aromaticity and diradical character for a variety of extended π-conjugated systems, including some salient recent examples of nanographenes and polycyclic aromatic radicals, are provided based on their [4n]annulene peripheries. The realization of such structure-property relationships has led to a beneficial pedagogic exercise establishing design guidelines for diradicaloids. The antiaromatic fingerprint of the [4n]annulene peripheries upon orbital interactions due to internal covalent connectors gives insights into the diradicaloid property of a diversity of π-conjugated molecules that have fascinated chemists recently.

The Transferability of Topologically Partitioned Electron Correlation Energies in Water Clusters

The electronic effects that govern the cohesion of water clusters are complex, demanding the inclusion of N-body, Coulomb, exchange and correlation effects. Here we present a much needed quantitative study of the effect of correlation (and hence dispersion) energy on the stabilization of water clusters. For this purpose we used a topological energy partitioning method called Interacting Quantum Atoms (IQA) to partition water clusters into topological atoms, based on a MP2/6-31G(d,p) wave function, and modified versions of GAUSSIAN09 and the Quantum Chemical Topology (QCT) program MORFI. Most of the cohesion in the water clusters provided by electron correlation comes from intramolecular energy stabilization. Hydrogen bond-related interactions tend to largely cancel each other. Electron correlation energies are transferable in almost all instances within 1 kcal mol^-1 . This observed transferability is very important to the further development of the QCT force field FFLUX, especially to the future modelling of liquid water.

The diverse manifold of electronic states generated by a single carbon defect in a graphene sheet: multireference calculations using a pyrene defect model

Detailed calculations have been performed on the electronic states occurring in a single vacancy defect model based on pyrene from which one of the central carbon atoms has been removed. Complete active space self-consistent field and multireference configuration interaction with singles and doubles calculations have been performed using the 6-31G and 6-31G* basis sets. Two types of defect geometries have been defined: 1) The unrelaxed defect structure based on pyrene and 2) a relaxed structure. In total 12 electronic states have been computed for the unrelaxed structure at C2v symmetry, comprising four singlets, triplets and quintets each. The lowest six states are formed from singlet and triplet states and appear in a rather narrow gap of ∼0.6 eV. The lowest quintet state is found 1.43 eV above the (3) B1 ground state. As predicted from Jahn-Teller distortions, a CC bond is formed between dangling carbon bonds in the (1, 3) B1 states, leading to the formation of a five-membered ring. The (1, 3) A2 states show initial repulsive behavior along the bond formation coordinate until an avoided crossing is reached by which these states are furnished with CC bonding character so that finally also in these cases a CC bond is established. Linear interpolation curves between the initial unrelaxed defect structure and the final optimized structure are used to give an overview of the evolution of electronic states and the occurrence of avoided crossings. Out-of-plane structures are investigated with special emphasis on the carbon atom containing a dangling bond in the relaxed structure. Unpaired electron densities are used to characterize the electronic structure of the different states.

On the basis set convergence of electron-electron entanglement measures: helium-like systems

A systematic investigation of three different electron–electron entanglement measures, namely the von Neumann, the linear and the occupation number entropy at full configuration interaction level has been performed for the four helium-like systems hydride, helium, Li⁺ and Be²⁺ using a large number of different basis sets. The convergence behavior of the resulting energies and entropies revealed that the latter do in general not show the expected strictly monotonic increase upon increase of the one–electron basis. Overall, the three different entanglement measures show good agreement among each other, the largest deviations being observed for small basis sets. The data clearly demonstrates that it is important to consider the nature of the chemical system when investigating entanglement phenomena in the framework of Gaussian type basis sets: while in case of hydride the use of augmentation functions is crucial, the application of core functions greatly improves the accuracy in case of cationic systems such as Li⁺ and Be²⁺. In addition, numerical derivatives of the entanglement measures with respect to the nucleic charge have been determined, which proved to be a very sensitive probe of the convergence leading to qualitatively wrong results (i.e., the wrong sign) if too small basis sets are used.

Atomic Partitioning of the MPn (n = 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA-MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Photoionization Observables from Multi-Reference Dyson Orbitals Coupled to B-Spline DFT and TD-DFT Continuum

We present a theoretical model to compute the accurate photoionization dynamical parameters (cross-sections, asymmetry parameters and orbital, or cross-section, ratios) from Dyson orbitals obtained with the multi-state complete active space perturbation theory to the second order (MS-CASPT2) method. Our new implementation of Dyson orbitals in OpenMolcas takes advantage of the full Abelian symmetry point group and has the corrected normalization. The Dyson orbitals are coupled to an accurate description of the electronic continuum obtained with a multicentric B-spline basis at the DFT and TD-DFT levels. Two prototype diatomic molecules, i.e., CS and SiS, have been chosen due to their smallness, which hides important correlation effects. These effects manifest themselves in the appearance of well-characterized isolated satellite bands in the middle of the valence region. The rich satellite structures make CS and SiS the perfect candidates for a computational study based on our highly accurate MS-CASPT2/B-spline TD-DFT protocol.

An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study of the Halogen Bond with Explicit Analysis of Electron Correlation

Energy profiles of seven halogen-bonded complexes were analysed with the topological energy partitioning called Interacting Quantum Atoms (IQA) at MP4(SDQ)/6-31+G(2d,2p) level of theory. Explicit interatomic electron correlation energies are included in the analysis. Four complexes combine X₂ (X = Cl or F) with HCN or NH₃, while the remaining three combine ClF with HCN, NH₃ or N₂. Each complex was systematically deformed by translating the constituent molecules along its central axis linking X and N, and reoptimising its remaining geometry. The Relative Energy Gradient (REG) method (Theor. Chem. Acc. 2017, 136, 86) then computes which IQA energies most correlate with the total energy during the process of complex formation and further compression beyond the respective equilibrium geometries. It turns out that the covalent energy (i.e., exchange) of the halogen bond, X…N, itself drives the complex formation. When the complexes are compressed from their equilibrium to shorter X…N distance then the intra-atomic energy of N is in charge. When the REG analysis is restricted to electron correlation then the interatomic correlation energy between X and N again drives the complex formation, and the complex compression is best described by the destabilisation of the through-space correlation energy between N and the "outer" halogen.

RI-MP3 calculations of biomolecules based on the fragment molecular orbital method

In this study, the third-order Møller-Plesset perturbation (MP3) theory using the resolution of the identity (RI) approximation was combined with the fragment molecular orbital (FMO) method to efficiently calculate a high-order electron correlation energy of biomolecular systems. We developed a new algorithm for the RI-MP3 calculation, which can be used with the FMO scheme. After test calculations using a small molecule, the FMO-RI-MP3 calculations were performed for two biomolecular systems comprising a protein and a ligand. The computational cost of these calculations was only around 5 and 4 times higher than those of the FMO-RHF calculations. The error associated with the RI approximation was around 2.0% of the third-order correlation contribution to the total energy. However, the RI approximation error in the interaction energy between the protein and ligand molecule was insignificantly small, which reflected the negligible error in the inter fragment interaction energy. © 2018 Wiley Periodicals, Inc.

Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z^HF_C=1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'.

Diversity of Chemical Bonding and Oxidation States in MS4 Molecules of Group 8 Elements

The geometric and electronic ground-state structures of 30 isomers of six MS₄ molecules (M=Group 8 metals Fe, Ru, Os, Hs, Sm, and Pu) have been studied by using quantum-chemical density functional theory and correlated wavefunction approaches. The MS₄ species were compared to analogous MO₄ species recently investigated (W. Huang, W.-H. Xu, W. H. E. Schwarz, J. Li, Inorg. Chem. 2016, 55, 4616). A metal oxidation state (MOS) with a high value of eight appeared in the low-spin singlet T_d geometric species (Os,Hs)S₄ and (Ru,Os,Hs)O₄ , whereas a low MOS of two appeared in the high-spin septet D_2d species Fe(S₂ )₂ and (slightly excited) metastable Fe(O₂ )₂ . The ground states of all other molecules had intermediate MOS values, with S^2- , S₂^2- , S₂^1- (and O^2- , O^1- , O₂^2- , O₂^1- ) ligands bonded by ionic, covalent, and correlative contributions. The known tendencies toward lower MOS on going from oxides to sulfides, from Hs to Os to Ru, and from Pu to Sm, and the specific behavior of Fe, were found to arise from the different atomic orbital energies and radii of the (n-1)p core and (n-1)d and (n-2)f valence shells of the metal atoms in row n of the periodic table. The comparative results of the electronic and geometric structures of the MO₄ and MS₄ species provides insight into the periodicity of oxidation states and bonding.

Recent progress in high-pressure studies on organic conductors

Recent high-pressure studies of organic conductors and superconductors are reviewed. The discovery of the highest T_c superconductivity among organics under high pressure has triggered the further progress of the high-pressure research. Owing to this finding, various organic conductors with the strong electron correlation were investigated under high pressures. This review includes the pressure techniques using the cubic anvil apparatus, as well as high-pressure studies of the organic conductors up to 10 GPa showing extraordinary temperature and pressure dependent transport phenomena.

The Coulomb Hole of the Ne Atom

We analyze the Coulomb hole of Ne from highly-accurate CISD wave functions obtained from optimized even-tempered basis sets. Using a two-fold extrapolation procedure we obtain highly accurate results that recover 97 % of the correlation energy. We confirm the existence of a shoulder in the short-range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the K-shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second-row atoms, thus confirming that it is due to K-shell correlation effects.

Electron correlation in Li+, He, H- and the critical nuclear charge system Z C : energies, densities and Coulomb holes

This paper presents high-accuracy correlation energies, intracule densities and Coulomb hole(s) for the lithium cation, helium, hydride ion and the system with the critical nuclear charge, Z C , for binding two electrons. The fully correlated (FC) wave function and the Hartree-Fock (HF) wave function are both determined using a Laguerre-based wave function. It is found that for the lithium cation and the helium atom a secondary Coulomb hole is present, in agreement with a previous literature finding, confirming a counterintuitive conclusion that electron correlation can act to bring distant electrons closer together. However, no evidence for a tertiary Coulomb hole is found. For the hydride anion and the system just prior to electron detachment only a single Coulomb hole is present and electron correlation decreases the probability of finding the electrons closer together at all radial distances. The emergence of a secondary Coulomb hole is investigated and found to occur between Z = 1.15 and Z = 1.20. The FC and HF energies and intracule densities (in atomic units) used to calculate the correlation energy and Coulomb hole, respectively, are accurate to at least the nano-scale for helium and the cation and at least the micro-scale for the anions.

Electron-Doping Mottronics in Strongly Correlated Perovskite

The discovery of hydrogen-induced electron localization and highly insulating states in d-band electron correlated perovskites has opened a new paradigm for exploring novel electronic phases of condensed matters and applications in emerging field-controlled electronic devices (e.g., Mottronics). Although a significant understanding of doping-tuned transport properties of single crystalline correlated materials exists, it has remained unclear how doping-controlled transport properties behave in the presence of planar defects. The discovery of an unexpected high-concentration doping effect in defective regions is reported for correlated nickelates. It enables electronic conductance by tuning the Fermi-level in Mott-Hubbard band and shaping the lower Hubbard band state into a partially filled configuration. Interface engineering and grain boundary designs are performed for H_x SmNiO₃ /SrRuO₃ heterostructures, and a Mottronic device is achieved. The interfacial aggregation of hydrogen is controlled and quantified to establish its correlation with the electrical transport properties. The chemical bonding between the incorporated hydrogen with defective SmNiO₃ is further analyzed by the positron annihilation spectroscopy. The present work unveils new materials physics in correlated materials and suggests novel doping strategies for developing Mottronic and iontronic devices via hydrogen-doping-controlled orbital occupancy in perovskite heterostructures.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited

A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.

Cyclobutadiene automerization and rotation of ethylene: energetics of the barriers by using spin-polarized wave functions

Spin-projected spin polarized Møller-Plesset and spin polarized coupled clusters calculations have been made to estimate the cyclobutadiene automerization, the ethylene torsion barriers in their ground state, and the gap between the singlet and triplet states of ethylene. The results have been obtained optimizing the geometries at MP4 and/or CCSD levels, by an extensive Gaussian basis set. A comparative analysis with more complex calculations, up to MP5 and CCSDTQP, together with others from the literature, have also been made, showing the efficacy of using spin-polarized wave functions as a reference wave function for Møller-Plesset and coupled clusters calculations, in such problems.

Cyclotron Resonance Study of Monolayer Graphene under Double Moiré Potentials

We report the first cyclotron resonance study of monolayer graphene under double-moiré potentials in which the crystal axis of graphene is nearly aligned to those of both the top and bottom hexagonal boron nitride (h-BN) layers. Under mid-infrared light irradiation, we observe cyclotron resonance absorption with the following unique features: (1) cyclotron resonance magnetic field B_CR is entirely different from that of nonaligned monolayer graphene, (2) B_CR exhibits strong electron-hole asymmetry, and (3) splitting of B_CR is observed for |ν| < 1, with the split maximum at |ν| = 1, resulting in eyeglass-shaped trajectories. These features are well explained by considering the large bandgap induced by the double moiré potentials, the electron-hole asymmetry in the Fermi velocity, and the Fermi-level-dependent enhancement of spin gaps, which suggests a large electron-electron correlation contribution in this system.