Pure and Hybrid SCAN, rSCAN, and r2SCAN: Which One Is Preferred in KS- and HF-DFT Calculations, and How Does D4 Dispersion Correction Affect This Ranking?

Using the large and chemically diverse GMTKN55 dataset, we have tested the performance of pure and hybrid KS-DFT and HF-DFT functionals constructed from three variants of the SCAN meta-GGA exchange-correlation functional: original SCAN, rSCAN, and r2SCAN. Without any dispersion correction involved, HF-SCANn outperforms the two other HF-DFT functionals. In contrast, among the self-consistent variants, SCANn and r2SCANn offer essentially the same performance at lower percentages of HF-exchange, while at higher percentages, SCANn marginally outperforms r2SCANn and rSCANn. However, with D4 dispersion correction included, all three HF-DFT-D4 variants perform similarly, and among the self-consistent counterparts, r2SCANn-D4 outperforms the other two variants across the board. In view of the much milder grid dependence of r2SCAN vs. SCAN, r2SCAN is to be preferred across the board, also in HF-DFT and hybrid KS-DFT contexts.

A Density Functional Theory Investigation of Intramolecular Dispersion Forces in Buckyball-Buckybowl Complexes

<p>The electron-rich, concave face of corannulene makes it an ideal candidate to host electron-deficient fullerenes, such as C60. The host–guest system is dominated by weak van derWaals interactions. Modelling of the C60@corannulene complex was carried out with nine different density functionals: B3LYP, B97-D, BP86, CAM-B3LYP, M06-2X, PW91, t-HCTH, wB97X, and wB97X-D, using the 6-31G(d) basis set. Results indicated that the functionals including an empirical dispersion correction term, B97-D and wB97X-D, gave the most reliable binding energy values when compared with ab initio SCS-MP2 benchmark computations. Additionally, a number of complexes with functionalised corannulene bowls were modelled at the wB97X-D/6-31G(d) level, with NMR calculations performed at the GIAO/wB97X-D/dec-6-31G(d) level. A linear trend was revealed between the number of substituents on corannulene and the strength of binding within complex with C60. Calculated 1H NMR Dd values for methyl groups on methyl substituted corannulene bowls were also linearly dependent on binding energy. Further results are reported here.</p>

A Density Functional Theory Investigation of Intramolecular Dispersion Forces in Buckyball-Buckybowl Complexes

<p>The electron-rich, concave face of corannulene makes it an ideal candidate to host electron-deficient fullerenes, such as C60. The host–guest system is dominated by weak van derWaals interactions. Modelling of the C60@corannulene complex was carried out with nine different density functionals: B3LYP, B97-D, BP86, CAM-B3LYP, M06-2X, PW91, t-HCTH, wB97X, and wB97X-D, using the 6-31G(d) basis set. Results indicated that the functionals including an empirical dispersion correction term, B97-D and wB97X-D, gave the most reliable binding energy values when compared with ab initio SCS-MP2 benchmark computations. Additionally, a number of complexes with functionalised corannulene bowls were modelled at the wB97X-D/6-31G(d) level, with NMR calculations performed at the GIAO/wB97X-D/dec-6-31G(d) level. A linear trend was revealed between the number of substituents on corannulene and the strength of binding within complex with C60. Calculated 1H NMR Dd values for methyl groups on methyl substituted corannulene bowls were also linearly dependent on binding energy. Further results are reported here.</p>

A New Type of Atmospheric Dispersion Corrector Suitable for Wide-Field High-Resolution Imaging and Spectroscopy on Large Telescopes

Atmospheric dispersion produces spectral elongation in images formed by land-based astronomical telescopes, and this elongation increases as the telescope points away from the zenith. Atmospheric Dispersion Correctors (ADCs) produce compensating dispersion that can be adjusted to best cancel out the atmospheric effect. These correctors are generally of two basic types: Rotating Atmospheric Dispersion Correctors (R-ADCs), and Linear Atmospheric Dispersion Correctors (L-ADCs). Lately, a third type, the “Compensating Lateral ADC” (CL-ADC) has been proposed. None of these design approaches allow for large corrector systems (with elements greater than 1 m in diameter), in which the secondary spectrum is corrected to small residuals, of the order of tens’ of milliarcseconds. This paper describes a new type of large corrector (>1 m diameter elements), which can achieve the correction of the secondary spectrum to the order of 10 milliarcseconds. This correction is achieved by combining the R-ADC and CL-ADC approaches to dispersion correction. Only glass types readily available in metre diameters are required.

Wavenumber-space band clipping in nonlinear periodic structures

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as an initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

Time dispersion correction for arbitrarily even-order Lax-Wendroff methods and the application on full waveform inversion

A second-order accurate finite-difference (FD) approximation is commonly used to approximate the second-order time derivative of wave equation. The second-order accurate FD scheme may introduce time dispersion in wavefield extrapolation. Lax-Wendroff methods can suppress such dispersion by replacing the high-order time FD error-terms with space FD error correcting terms. However, the time dispersion cannot be completely eliminated and the computation cost dramatically increases with increasing order of (temporal) accuracy. To mitigate the problem, we extend the existing time dispersion correction scheme for second- or fourth-order Lax-Wendroff method to a scheme for arbitrary even-order methods, which uses the forward and inverse time dispersion transform (FTDT and ITDT) to add and remove the time dispersion from synthetic data. We test the correction scheme using a homogeneous model and the Sigsbee2A model. Modeling examples suggest that the use of derived FTDT and ITDT pairs on high-order Lax-Wendroff methods can effectively remove time dispersion errors from high-frequency waves while using longer time steps than allowed in low-order Lax-Wendroff methods. We investigate the influence of the time dispersion on full waveform inversion (FWI) and show an anti-dispersion workflow. We apply the FTDT to source terms and recorded traces before inversion, resulting in that the source and adjoint wavefields contain equal time dispersion from source-side wave propagation, and the modeled and observed traces accumulate equal time dispersion from source- and receiver-side wave propagation. Inversion results reveal that the anti-dispersion workflow is capable of increasing the accuracy of FWI for arbitrary even-order Lax-Wendroff methods. Additionally, the high-order method can obtain better inversion results compared to the second-order method with the same anti-dispersion workflow.

Ru-Doped Single Walled Carbon Nanotubes as Sensors for SO2 and H2S Detection

Carbon nanotubes are of great interest for their ability to functionalize with atoms for adsorbing toxic gases such as CO, NO, and NO2. Here, we use density functional theory in conjunction with dispersion correction to examine the encapsulation and adsorption efficacy of SO2 and H2S molecules by a (14,0) carbon nanotube and its substitutionally doped form with Ru. Exoergic encapsulation and adsorption energies are calculated for pristine nanotubes. The interaction of molecules with pristine nanotube is non-covalent as confirmed by the negligible charge transfer. The substitutional doping of Ru does not improve the encapsulation significantly. Nevertheless, there is an important enhancement in the adsorption of molecules by Ru-doped (14,0) nanotube. Such strong adsorption is confirmed by the strong chemical interaction between the nanotube and molecules. The promising feature of Ru-doped nanotubes can be tested experimentally for SO2 and H2S gas sensing.