Small Gap Systems Research Articles

Repartitioned Brillouin-Wigner perturbation theory with a size-consistent second-order correlation energy.

Second-order Møller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size consistency and extensivity, severely limiting its application to chemistry. In this work, we propose an alternative partitioning of the Hamiltonian that leads to a regular BWPT perturbation series that, through the second order, is size-extensive, size-consistent (provided its Hartree-Fock reference is also), and orbital invariant. Our second-order size-consistent Brillouin-Wigner (BW-s2) approach can describe the exact dissociation limit of H2 in a minimal basis set, regardless of the spin polarization of the reference orbitals. More broadly, we find that BW-s2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, although rivaling coupled-cluster with single and double substitutions for thermochemical properties.

Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling

High-harmonic generation (HHG) in solids is a fundamental nonlinear phenomenon, which can be efficiently controlled by modifying system parameters such as doping-level and temperature. In order to correctly predict the dependence of HHG on these parameters, consistent theoretical formulation of the light-matter coupling is crucial. Recently, contributions to the current that are often missing in the HHG analysis based on the semiconductor Bloch equations have been pointed out [J. Wilhelm, et.al. PRB 103 125419 (2021)]. In this paper, by systematically analyzing the doping and gap-size dependence of HHG in gapped graphene, we discuss the practical impact of such terms. In particular, we focus on the role of the current $J_{\rm ra}^{(2)}$, which originates from the change of the intraband dipole via interband transition. When the gap is small and the system is close to half filling, intraband and interband currents mostly cancel, thus suppressing the HHG signal - an important property that is broken when neglecting $J_{\rm ra}^{(2)}$. Furthermore, without $J_{\rm ra}^{(2)}$, the doping and gap-size dependence of HHG becomes qualitatively different from the full evaluation. Our results demonstrate the importance of the consistent expression of the current to study the parameter dependence of HHG for the small gap systems.

Opto-electronic properties of twisted bilayer graphene quantum dots

The electronic and interband optical properties of vertically coupled stacked graphene quantum dots are investigated using the tight-binding method. Both zigzag and armchair edge configurations are taken into account. In particular, the effect of the geometrical shape (triangular or circle-like) and, most prominently, of the angle of twisting between layers is mainly addressed. The optical response is analyzed from the calculated imaginary part of the dielectric function. It is found that the interband absorption threshold is highly dependent on the dot size and geometry: For armchair triangular bilayer graphene dots the optical gap exhibits a moderate increase for smaller angles of twisting, and the structure behaves as an intermediate to a wide gap semiconductor; whereas zigzag triangular bilayer graphene dots are small gap systems in which the twisting causes the appearance of zero-gap states associated with the variation of HOMO and LUMO states resulting from the breaking of zero-energy degeneracy. In the latter case, it is shown that the low-energy transitions between those states are responsible for the main optical response of the structures which indicates possible applications in the THz optoelectronics. Circular dots are chosen in commensurable configurations and also show stronger low-energy absorption thresholds. A particular feature appearing in this case is the presence of Bravais-Moiré patterns in the two-dimensional probability density distributions for large enough dot radii.

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)

In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).

Random-Phase Approximation Methods.

Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.

Minding the Gap: Synthetic Strategies for Tuning the Energy Gap in Conjugated Molecules

While structure–property relationships are commonly developed in applications of physical organic chemistry to real-world problems at the graduate level, they have not been generally emphasized in the undergraduate chemistry curriculum. For instance, the ability to modify the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in π-conjugated small molecules and polymers is of particular interest in the fields of polymer chemistry and materials science, where small-gap systems can function as semiconductors in electronic devices. In order to demonstrate a general strategy for tuning the HOMO–LUMO energy gap for π-conjugated materials, a new experiment was designed for the undergraduate organic laboratory course that combines synthesis with theoretical calculations for π-conjugated biphenyl systems with differing electronic properties to generate a simple structure–property study of functional group substitution on the biphenyl core. The synth...

Screened exchange hybrid density functional for accurate and efficient structures and interaction energies.

We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.

A Survey of Wireless Power Transfer and a Critical Comparison of Inductive and Capacitive Coupling for Small Gap Applications

Inductive power transfer (IPT) and capacitive power transfer (CPT) are the two most pervasive methods of wireless power transfer (WPT). IPT is the most common and is applicable to many power levels and gap distances. Conversely, CPT is only applicable for power transfer applications with inherently small gap distances due to constraints on the developed voltage. Despite limitations on gap distance, CPT has been shown to be viable in kilowatt power level applications. This paper provides a critical comparison of IPT and CPT for small gap applications, wherein the theoretical and empirical limitations of each approach are established. A survey of empirical WPT data across diverse applications in the last decade using IPT and CPT technology graphically compares the two approaches in power level, gap distance, operational frequency, and efficiency, among other aspects. The coupler volumetric power density constrained to small gap sizes is analytically established through theoretical physical limitations of IPT and CPT. Finally, guidelines for selecting IPT or CPT in small gap systems are presented.

Analytical First-Order Molecular Properties and Forces within the Adiabatic Connection Random Phase Approximation.

The random phase approximation (RPA) is an increasingly popular method for computing molecular ground-state correlation energies within the adiabatic connection fluctuation-dissipation theorem framework of density functional theory. We present an efficient analytical implementation of first-order RPA molecular properties and nuclear forces using the resolution-of-the-identity (RI) approximation and imaginary frequency integration. The centerpiece of our approach is a variational RPA energy Lagrangian invariant under unitary transformations of occupied and virtual reference orbitals, respectively. Its construction requires the solution of a single coupled-perturbed Kohn-Sham equation independent of the number of perturbations. Energy gradients with respect to nuclear displacements and other first-order properties such as one-particle densities or dipole moments are obtained from partial derivatives of the Lagrangian. Our RPA energy gradient implementation exhibits the same [Formula: see text] scaling with system size N as a single-point RPA energy calculation. In typical applications, the cost for computing the entire gradient vector with respect to nuclear displacements is ∼5 times that of a single-point RPA energy calculation. Derivatives of the quadrature nodes and weights used for frequency integration are essential for RPA gradients with an accuracy consistent with RPA energies and can be included in our approach. The quality of RPA equilibrium structures is assessed by comparison to accurate theoretical and experimental data for covalent main group compounds, weakly bonded dimers, and transition metal complexes. RPA outperforms semilocal functionals as well as second-order Møller-Plesset (MP2) theory, which fails badly for the transition metal compounds. Dipole moments of polarizable molecules and weakly bound dimers show a similar trend. RPA harmonic vibrational frequencies are nearly of coupled cluster singles, doubles, and perturbative triples quality for a set of main group compounds. Compared to the ring-coupled cluster based implementation of Rekkedal et al. [J. Chem. Phys. 2013, 139, 081101.], our method scales better by two powers of N and supports a semilocal Kohn-Sham reference. The latter is essential for the good performance of RPA in small-gap systems.

Communication: Random phase approximation renormalized many-body perturbation theory

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

Flow-Induced Instability on High-Speed Mini Rotors in Laminar Flow

In this study, a modeling approach is developed to examine laminar flow effects on the rotordynamic behavior of high-speed mini rotating machinery with a moderate flow confinement. The existing research work mostly focuses on the flow-induced forces in small gap systems, such as bearings and seals, in which the flow is mostly laminar and inertia effects are ignored. In other studies, medium gap systems are analyzed, taking the inertia effects into consideration, but the surrounding flow is considered as turbulent. However, in high speed mini rotating machinery, the large clearances and the high speeds make the inertia effects significant, even in the laminar flow regime. In the current study, the flow-induced forces resulting from the surrounding fluid are analyzed and these models are combined with the structural finite element (FE) models for determining the rotordynamic behavior. The structure is analyzed with finite elements based on Timoshenko beam theory. Flow-induced forces, which include inertia effects, are implemented into the structure as added mass-stiffness-damping at each node in the fluid confinement. The shear stress is modeled with empirical and analytical friction coefficients, and the stability, critical speeds, and vibration response of the rotor is investigated for different friction models. In order to validate the developed modeling approach, experiments were conducted on a specially designed setup at different support properties. By comparing the experiments with the theoretical models, the applicability of the different friction models are examined. It was found that the dynamic behavior is estimated better with empirical friction models compared to using the analytical friction models.

Second-order Møller–Plesset perturbation theory applied to extended systems. II. Structural and energetic properties

Results for the lattice constants, atomization energies, and band gaps of typical semiconductors and insulators are presented for Hartree-Fock and second-order Moller-Plesset perturbation theory (MP2). We find that MP2 tends to undercorrelate weakly polarizable systems and overcorrelates strongly polarizable systems. As a result, lattice constants are overestimated for large gap systems and underestimated for small gap systems. The volume dependence of the MP2 correlation energy and the dependence of the MP2 band gaps on the static dielectric screening properties are discussed in detail. Moreover, the relationship between MP2 and the G(0)W(0) quasiparticle energies is elucidated and discussed. Finally, we demonstrate explicitly that the correlation energy diverges with decreasing k-point spacing for metals.

Dispersion interactions between semiconducting wires

The dispersion energy between extended molecular chains (or equivalently infinite wires) with non-zero band gaps is generally assumed to be expressible as a pair-wise sum of atom-atom terms which decay as $R^{-6}$. Using a model system of two parallel wires with a variable band gap, we show that this is not the case. The dispersion interaction scales as $z^{-5}$ for large interwire separations $z$, as expected for an insulator, but as the band gap decreases the interaction is greatly enhanced; while at shorter (but non-overlapping) separations it approaches a power-law scaling given by $z^{-2}$, \emph{i.e.} the dispersion interaction expected between \emph{metallic} wires. We demonstrate that these effects can be understood from the increasing length scale of the plasmon modes (charge fluctuations), and their increasing contribution to the molecular dipole polarizability and the dispersion interaction, as the band gaps are reduced. This result calls into question methods which invoke locality assumptions in deriving dispersion interactions between extended small-gap systems.

Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N(4) log N) operations and O(N(3)) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield muH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

Comparative study of the sagittal elastic waves in metallic and semiconductor multilayer systems between periodic and Fibonacci superlattices

We study the sagittal elastic waves in periodic and Fibonacci superlattices by means of the frequency dispersion relation and the density of states. We study also the intermediate multilayer structures between both systems, which can be seen as periodic or Fibonacci systems with planar defects. Applications are made to specific metallic and semiconductor systems as representative of the wide gap and small gap systems, respectively, in order to see the influence of the different elastic properties on the gaps and acoustic properties of these multilayer systems.