Bending Two-Dimensional Materials To Control Charge Localization and Fermi-Level Shift

High-performance electronics requires the fine control of semiconductor conductivity. In atomically thin two-dimensional (2D) materials, traditional doping technique for controlling carrier concentration and carrier type may cause crystal damage and significant mobility reduction. Contact engineering for tuning carrier injection and extraction and carrier type may suffer from strong Fermi-level pinning. Here, using first-principles calculations, we predict that mechanical bending, as a unique attribute of thin 2D materials, can be used to control conductivity and Fermi-level shift. We find that bending can control the charge localization of top valence bands in both MoS₂ and phosphorene nanoribbons. The donor-like in-gap edge-states of armchair MoS₂ ribbon and their associated Fermi-level pinning can be removed by bending. A bending-controllable new in-gap state and accompanying direct–indirect gap transition are predicted in armchair phosphorene nanoribbon. We demonstrate that such emergent bending effects are realizable. The bending stiffness as well as the effective thickness of 2D materials are also derived from first principles. Our results are of fundamental and technological relevance and open new routes for designing functional 2D materials for applications in which flexuosity is essential

Density Functional Theory Study of Controllable Optical Absorptions and Magneto-Optical Properties of Magnetic CrI₃ Nanoribbons: Implications for Compact 2D Magnetic Devices

A chromium triiodide (CrI3) monolayer has an interesting ferromagnetic ground state. In this work, we calculate band structures and magnetic moments of tensile-strained and bent zigzag CrI3 nanoribbons with density functional theory. The edge iodine atoms form flat low-lying conduction bands and couple with chromium atoms ferromagnetically, while the non-edge iodine atoms weakly couple antiferromagnetically. Narrow CrI3 nanoribbons have two locally stable magnetic moment orientations, namely, out-of-plane and in-plane (along the nanoribbon periodic direction) configurations. This enables four magnetization states in CrI3 nanoribbons, including two out-of-plane ones (up and down) and two in-plane ones (forward and backward along the nanoribbon periodical direction), increasing the operating controllability. Based on the one-dimensional Ising spin chain model, the spin correlation length of the narrow CrI3 nanoribbon is estimated to be about 10 Å at its estimated Curie temperature of 27 K, which is lower than the measured 45 K of the monolayer CrI3. The optical absorption and magneto-optical properties of CrI3 nanoribbons are investigated with many-body perturbation GW-BSE (Bethe–Salpeter equation), including magnetic dichroism and Faraday and magneto-optical Kerr effects. The low-energy dark excitons are mainly from transitions between electrons and holes with unlike spins and are non-Frenkel-like, while the bright excitons have mixed spin configurations. The intrinsic lifetime of excitons can be over one nanosecond, suitable for quantum information processes. Tensile strains and bending manifestly modulate the absorption spectra and magneto-optical properties of CrI3 nanoribbons within a technologically important photon energy range of ∼1.0–2.0 eV. The CrI3 nanoribbons can be used in 1D or 2D magnetic storage nanodevices, tunable magnetic optoelectronics, and spin-based quantum information controls

Accurate Complete Basis Set Extrapolation of Direct Random Phase Correlation Energies

The direct random phase approximation (dRPA) is a promising way to obtain improvements upon the standard semilocal density functional results in many aspects of computational chemistry. In this paper, we address the slow convergence of the calculated dRPA correlation energy with the increase of the quality and size of the popular Gaussian-type Dunning’s correlation consistent aug-cc-pV<i>X</i>Z split valence atomic basis set family. The cardinal number <i>X</i> controls the size of the basis set, and we use <i>X</i> = 3–6 in this study. It is known that even the very expensive <i>X</i> = 6 basis sets lead to large errors for the dRPA correlation energy, and thus complete basis set extrapolation is necessary. We study the basis set convergence of the dRPA correlation energies on a set of 65 hydrocarbon isomers from CH₄ to C₆H₆. We calculate the iterative density fitted dRPA correlation energies using an efficient algorithm based on the CC-like form of the equations using the self-consistent HF orbitals. We test the popular inverse cubic, the optimized exponential, and inverse power formulas for complete basis set extrapolation. We have found that the optimized inverse power based extrapolation delivers the best energies. Further analysis showed that the optimal exponent depends on the molecular structure, and the most efficient two-point energy extrapolations that use <i>X</i> = 3 and 4 can be improved considerably by considering the atomic composition and hybridization states of the atoms in the molecules. Our results also show that the optimized exponents that yield accurate <i>X</i> = 3 and 4 extrapolated dRPA energies for atoms or small molecules might be inaccurate for larger molecules

Adiabatic Connection without Coupling Constant Integration

Using a second-order approximation to Random Phase Approximation renormalized (RPAr) many-body perturbation theory for the interacting density–density response function, we have developed a so-called higher-order terms (HOT) approximation for the correlation energy. In combination with the first-order RPAr correction, our new method faithfully captures the infinite-order correlation for a given exchange-correlation kernel, yielding errors of the total correlation energy on the order of 1% or less for most systems. For exchange-like kernels, our new method has the further benefit that the coupling-strength integration can be completely eliminated resulting in a modest reduction in computational cost compared to the traditional approach. When the correlation energy is accurately reproduced by the HOT approximation, structural properties and energy differences are also accurately reproduced, as we demonstrate for several periodic solids and some molecular systems. Energy differences involving fragmentation are challenging for the HOT method, however, due to errors that may not cancel between a composite system and its constituent pieces

A meta-GGA Made Free of the Order of Limits Anomaly

We have improved the revised Tao–Perdew–Staroverov–Scuseria (revTPSS) meta-generalized gradient approximation (GGA) in order to remove the order of limits anomaly in its exchange energy. The revTPSS meta-GGA recovers the second-order gradient expansion for a wide range of densities and therefore provides excellent atomization energies and lattice constants. For other properties of materials, however, even the revTPSS does not give the desired accuracy. The revTPSS does not perform as well as expected for the energy differences between different geometries for the same molecular formula and for the related nonbarrier height chemical reaction energies. The same order of limits problem might lead to inaccurate energy differences between different crystal structures and to inaccurate cohesive energies of insulating solids. Here we show a possible way to remove the order of limits anomaly with a weighted difference of the revTPSS exchange between the slowly varying and iso-orbitals (one- or two-electron) limits. We show that the new regularized (regTPSS) gives atomization energies comparable to revTPSS and preserves the accurate lattice constants as well. For other properties, the regTPSS gives at least the same performance as the revTPSS or TPSS meta-GGAs

Construction and Application of a New Dual-Hybrid Random Phase Approximation

The direct random phase approximation (dRPA) combined with Kohn–Sham reference orbitals is among the most promising tools in computational chemistry and applicable in many areas of chemistry and physics. The reason for this is that it scales as <i>N</i>⁴ with the system size, which is a considerable advantage over the accurate ab initio wave function methods like standard coupled-cluster. dRPA also yields a considerably more accurate description of thermodynamic and electronic properties than standard density-functional theory methods. It is also able to describe strong static electron correlation effects even in large systems with a small or vanishing band gap missed by common single-reference methods. However, dRPA has several flaws due to its self-correlation error. In order to obtain accurate and precise reaction energies, barriers and noncovalent intra- and intermolecular interactions, we construct a new dual-hybrid dRPA (hybridization of exact and semilocal exchange in both the energy and the orbitals) and test the performance of this new functional on isogyric, isodesmic, hypohomodesmotic, homodesmotic, and hyperhomodesmotic reaction classes. We also use a test set of 14 Diels–Alder reactions, six atomization energies (AE6), 38 hydrocarbon atomization energies, and 100 reaction barrier heights (DBH24, HT-BH38, and NHT-BH38). For noncovalent complexes, we use the NCCE31 and S22 test sets. To test the intramolecular interactions, we use a set of alkane, cysteine, phenylalanine-glycine-glycine tripeptide, and monosaccharide conformers. We also discuss the delocalization and static correlation errors. We show that a universally accurate description of chemical properties can be provided by a large, 75% exact exchange mixing both in the calculation of the reference orbitals and the final energy

Construction of a Spin-Component Scaled Dual-Hybrid Random Phase Approximation

Recently, we have constructed a dual-hybrid direct random phase approximation method, called dRPA75, and demonstrated its good performance on reaction energies, barrier heights, and noncovalent interactions of main-group elements. However, this method has also shown significant but quite systematic errors in the computed atomization energies. In this paper, we suggest a constrained spin-component scaling formalism for the dRPA75 method (SCS-dRPA75) in order to overcome the large error in the computed atomization energies, preserving the good performance of this method on spin-unpolarized systems at the same time. The SCS-dRPA75 method with the aug-cc-pVTZ basis set results in an average error lower than 1.5 kcal mol^–1 for the entire <i>n</i>-homodesmotic hierarchy of hydrocarbon reactions (RC0–RC5 test sets). The overall performance of this method is better than the related direct random phase approximation-based double-hybrid PWRB95 method on open-shell systems of main-group elements (from the GMTKN30 database) and comparable to the best <i>O</i>(<i>N</i>⁴)-scaling opposite-spin second-order perturbation theory-based double-hybrid methods like PWPB95-D3 and to the <i>O</i>(<i>N</i>⁵)-scaling RPAX2@PBEx method, which also includes exchange interactions. Furthermore, it gives well-balanced performance on many types of barrier heights similarly to the best <i>O</i>(<i>N</i>⁵)-scaling second-order perturbation theory-based or spin-component scaled second-order perturbation theory-based double-hybrid methods such as XYG3 or DSD-PBEhB95. Finally, we show that the SCS-dRPA75 method has reduced self-interaction and delocalization errors compared to the parent dRPA75 method and a slightly smaller static correlation error than the related PWRB95 method

Accurate, Precise, and Efficient Theoretical Methods To Calculate Anion−π Interaction Energies in Model Structures

A correct description of the anion−π interaction is essential for the design of selective anion receptors and channels and important for advances in the field of supramolecular chemistry. However, it is challenging to do accurate, precise, and efficient calculations of this interaction, which are lacking in the literature. In this article, by testing sets of 20 binary anion−π complexes of fluoride, chloride, bromide, nitrate, or carbonate ions with hexafluorobenzene, 1,3,5-trifluorobenzene, 2,4,6-trifluoro-1,3,5-triazine, or 1,3,5-triazine and 30 ternary π–anion−π′ sandwich complexes composed from the same monomers, we suggest domain-based local-pair natural orbital coupled cluster energies extrapolated to the complete basis-set limit as reference values. We give a detailed explanation of the origin of anion−π interactions, using the permanent quadrupole moments, static dipole polarizabilities, and electrostatic potential maps. We use symmetry-adapted perturbation theory (SAPT) to calculate the components of the anion−π interaction energies. We examine the performance of the direct random phase approximation (dRPA), the second-order screened exchange (SOSEX), local-pair natural-orbital (LPNO) coupled electron pair approximation (CEPA), and several dispersion-corrected density functionals (including generalized gradient approximation (GGA), meta-GGA, and double hybrid density functional). The LPNO-CEPA/1 results show the best agreement with the reference results. The dRPA method is only slightly less accurate and precise than the LPNO-CEPA/1, but it is considerably more efficient (6–17 times faster) for the binary complexes studied in this paper. For 30 ternary π–anion−π′ sandwich complexes, we give dRPA interaction energies as reference values. The double hybrid functionals are much more efficient but less accurate and precise than dRPA. The dispersion-corrected double hybrid PWPB95–D3­(BJ) and B2PLYP–D3­(BJ) functionals perform better than the GGA and meta-GGA functionals for the present test set

Performance of meta-GGA Functionals on General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions

Among the computationally efficient semilocal density functionals for the exchange-correlation energy, meta-generalized-gradient approximations (meta-GGAs) are potentially the most accurate. Here, we assess the performance of three new meta-GGAs (revised Tao–Perdew–Staroverov–Scuseria or revTPSS, regularized revTPSS or regTPSS, and meta-GGA made simple or MGGA_MS), within and beyond their “comfort zones,” on Grimme’s big test set of main-group molecular energetics (thermochemistry, kinetics, and noncovalent interactions). We compare them against the standard Perdew–Burke–Ernzerhof (PBE) GGA, TPSS, and Minnesota M06L meta-GGAs, and Becke-3-Lee–Yang–Parr (B3LYP) hybrid of GGA with exact exchange. The overall performance of these three new meta-GGA functionals is similar. However, dramatic differences occur for different test sets. For example, M06L and MGGA_MS perform best for the test sets that contain noncovalent interactions. For the 14 Diels–Alder reaction energies in the “difficult” DARC subset, the mean absolute error ranges from 3 kcal mol^–1 (MGGA_MS) to 15 kcal mol^–1 (B3LYP), while for some other reaction subsets the order of accuracy is reversed; more generally, the tested new semilocal functionals outperform the standard B3LYP for ring reactions. Some overall improvement is found from long-range dispersion corrections for revTPSS and regTPSS but not for MGGA_MS. Formal and universality criteria for the functionals are also discussed