scholarly journals The Convergence of the Legendre–Galerkin Spectral Method for Constructing Atmospheric Acoustic Normal Modes

2020 ◽  
Vol 28 (03) ◽  
pp. 2050002
Author(s):  
Richard B. Evans
Keyword(s):  
Legendre Polynomials ◽  
Normal Modes ◽  
Sobolev Norm ◽  
Linear Operators ◽  
Basis Sets ◽  
Spectral Approximation ◽  
Spectral Approximations ◽  
Potential Applications ◽  
Galerkin Spectral Method ◽  
Theoretical Results

The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the [Formula: see text] Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues are simple. Numerical results that help interpret the theory are presented. Eigenvalues corresponding to acoustic modes with smaller [Formula: see text] norms are especially accurately approximated, even with lower dimensioned basis sets of Legendre polynomials. The deficiencies in the potential applications of the theoretical results are noted in connection with the numerical examples.

First-Principles Study of Triangle Terarylene as a Possible Optical Molecular Switch

2011 ◽  
Vol 311-313 ◽  
pp. 526-529
Author(s):  
Cai Juan Xia ◽  
Han Chen Liu ◽  
Ji Xin Yin
Keyword(s):  
First Principles ◽  
Density Functional ◽  
Molecular Switch ◽  
Optical Switches ◽  
Functional Theory ◽  
Closed Ring ◽  
Potential Applications ◽  
Homo Lumo ◽  
Non Equilibrium Green’S Function ◽  
Theoretical Results

Using non-equilibrium Green’s function formalism combined with first-principles density functional theory, we investigate the electronic transport properties of a triangle terarylene(open- and closed-ring forms) optical molecular switch. The influence of the HOMO-LUMO gaps and the spatial distributions of molecular orbitals on the quantum transport through the molecular device is discussed. Theoretical results show that the conductance of the closed-ring is 3-8 times larger than that of open-ring, which expect that this system can be one of good candidates for optical switches due to this unique advantage, and may have some potential applications in future molecular circuit.

Photocatalytic application of Graphene oxide-ZnO nanocomposite for the reduction of methylene blue dye

2021 ◽  
Author(s):  
Bansura Banu ◽  
Mercy Jennifer ◽  
Udith Ferdila
Keyword(s):  
Methylene Blue ◽  
Graphene Oxide ◽  
Charge Transfer ◽  
Density Of States ◽  
Density Functional ◽  
Basis Sets ◽  
Blue Dye ◽  
Layer Spacing ◽  
Photocatalytic Application ◽  
Theoretical Results

Abstract The Graphene Oxide (GO) and GO-Zinc Oxide (GO-ZnO) nanocomposite were prepared using simplified techniques with modified Hummer’s and solvothermal methods for photocatalytic application. In a comparative study, the optimized geometries, binding energies, electronic properties, non-linear optical properties and density of states of GO-ZnO were calculated using density functional theory (DFT) calculations with B3LYP method at 6-31G (d,p) and LanL2DZ basis sets to examine the binding site of a methylene blue (MB) dye systematically. The result of Natural bond orbital (NBO) analysis revealed the effective charge transfer and also explained the mechanism and efficiency of the photocatalytic activity of GO-ZnO. Density of states supported the strong interaction of MB with the GO-ZnO leading to the degradation of the MB dye. The attained theoretical results depict the existence of n → σ*, n → n* and σ → σ* interactions, improved charge transfer, reduced band gap which establish the use of GO-ZnO in the visible light photocatalytic performance. Characterization methods such as XRD, FTIR and UV were carried out to support our theoretical results. The XRD results confirmed the particle size of 21 nm with inter layer spacing of 0.87 nm. FTIR spectroscopy indicated the characteristic bands related to the elements in GO-ZnO. The higher electrical conductivity is studied using UV-Vis spectral analysis. The calculated results show good agreements with experimental observations reveal that the GO-ZnO has good photocatalytic behavior.

Quantum-Chemical Ab Initio Calculations on Inda- and Thallabenzene (C5H5In and C5H5Tl) and their Structural Isomers η5-C5H5In and η5-C5H5Tl

2018 ◽  
Vol 71 (3) ◽  
pp. 102
Author(s):  
Emma Persoon ◽  
Yuekui Wang ◽  
Gerhard Raabe
Keyword(s):  
Ab Initio ◽  
Quantum Chemical ◽  
Density Functional ◽  
Single Point ◽  
Normal Modes ◽  
Dft Method ◽  
Basis Sets ◽  
Triplet States ◽  
Structural Isomers ◽  
Td Dft

Quantum-chemical ab initio, time-independent, as well as time-dependent density functional theory (TD-DFT) calculations were performed on the so far elusive heterocycles inda- and thallabenzene (C5H5In and C5H5Tl), employing several different methods (MP2, CISD, CCSD, CCSD(T), BD, BD(T), QCISD, QCISD(T), CASSCF, DFT/B3LYP), effective core potentials, and different basis sets. While calculations on the MP2 level predict the ground states of the title compounds to be singlets with the first triplet states between 13 and 15 kcal mol−1 higher in energy, single point calculations with the QCISD(T), CCSD(T), and BD(T) methods at CCSD-optimized structures result in energy differences between the singlet and the triplet states in the range between 0.3 and 2.1 kcal mol−1 in favour of the triplet states. According to a CASSCF(8,8) calculation the triplets are also more stable by about 2.5–2.9 kcal mol−1. Calculations were also performed for the C5v-symmetric η5 structural isomers (cyclopentadienylindium, CpIn, and cyclopentadienylthallium, CpTl, Cp = C5H5) of the title compounds. At the highest level of theory employed in this study, C5H5In is between 79 and 88 kcal mol−1 higher in energy than CpIn, while this energy difference is even larger for thallabenzene where C5H5Tl is energetically between 94 and 102 kcal mol−1 above CpTl. In addition we report on the UV/vis spectra calculated with a TD-DFT method as well as on the spectra of the normal modes of C5H5In and C5H5Tl. Both types of spectra might facilitate identification of the title compounds eventually formed in photolysis or pyrolysis experiments.

scholarly journals Computing Effective Hamiltonians of Coupled Electromagnetic Systems

2021 ◽  
Author(s):  
Shaolin Liao ◽  
Lu Ou
Keyword(s):  
Boundary Condition ◽  
Dispersion Relation ◽  
Normal Modes ◽  
Computational Procedure ◽  
Hamiltonian Matrix ◽  
Effective Hamiltonian ◽  
Electromagnetic System ◽  
Wave Dynamics ◽  
Potential Applications ◽  
Free Port

In this paper, we present an efficient procedure to compute the effective Hamiltonian matrix of a coupled electromagnetic system consisting of subsystems that are coupled to a discrete number of channels through couplers. Each subsystem is described by its own effective non-Hermitian Hamiltonian and the corresponding Quasi-normal Modes (QNMs), while the coupler connecting the subsystems and the channels is described by the scattering matrix, which is equivalent to the transfer matrix, in terms of port vectors defined for the coupler. Due to the constraints imposed by the QNMs of the subsystems and the wave dynamics of the channels, as well as boundary condition constraints, constraint-free port vectors need to be chosen efficiently and they follow two rules: 1) port vectors forming loops with couplers; 2) port vectors of couplers with most constraints or with less freedom. With the constraint-free port vectors chosen, the effective Hamiltonian matrix of the coupled electromagnetic system can be obtained by imposing the boundary condition constraints. After the effective Hamiltonian is obtained, the eigenvalues, eigenvectors and dispersion relation of the coupled electromagnetic system, as well as other quantities such as the reflection and transmission, can be calculated. A 2D interstitial square coupled MRRs array is used as an example to demonstrate the computational procedure. The computation of the effective Hamiltonian matrix of a coupled electromagnetic system has many potential applications such as MRRs array, coupled Parity-Time Non-Hermitian electromagnetic system, as well as the dispersion relation of finite and infinite arrays.

A Legendre-Galerkin spectral method for constructing atmospheric acoustic normal modes

2018 ◽  
Vol 143 (6) ◽  
pp. 3595-3601 ◽  
Author(s):  
Richard B. Evans ◽  
Xiao Di ◽  
Kenneth E. Gilbert
Keyword(s):  
Spectral Method ◽  
Normal Modes ◽  
Galerkin Spectral Method

Quantum-Chemical Ab Initio Calculations on Ala-(C5H5Al) and Galabenzene (C5H5Ga)

2014 ◽  
Vol 69 (7) ◽  
pp. 349-359 ◽  
Author(s):  
Stefanie Mersmann ◽  
Halima Mouhib ◽  
Matthias Baldofski ◽  
Gerhard Raabe
Keyword(s):  
Ab Initio ◽  
Quantum Chemical ◽  
Density Functional ◽  
Normal Modes ◽  
Closed Shell ◽  
Basis Sets ◽  
Moderate Intensity ◽  
Spectral Curves ◽  
Singlet States ◽  
Td Dft

1Quantum-chemical ab initio and time-dependent density functional theory (TD-DFT) calculations employing various basis sets were used to elucidate the spatial as well as the electronic structure of C5H5Al () and C5H5Ga (2) (ala- and galabenzene). The lowest closed shell singlet states of both compounds were found to have a non-planar structure of CS symmetry with C-X-C bond angles of about 116° (MP2/6-311++G**) and 125° (CCSD/aug-cc-pVDZ). At approximately 103°, the corresponding angles of the lowest triplets are significantly smaller. The lowest triplet state of alabenzene is also non-planar (CS) at the MP2 level while optimization with the CCSD and the CASPT2 method resulted in planar structures with C2v symmetry. The corresponding state of galabenzene has C2v symmetry at all levels of optimization. The relative stability of the lowest closed shell singlet and the lowest triplet (ΔE(T1-S0)) state is small and its sign even strongly method-dependent. However, according to the highest levels of theory applied in this study the singlet states of both molecules are slightly lower in energy than the corresponding triplets with singlet/triplet gaps between about 0.5 and 5.8 kcal/mol in favour of the singlet states. Most of the applied methods give a slightly smaller splitting for ala- than for galabenzene. Independent of the applied method (TD-DFT/CAM-B3LYP/6-311++G(3df,3pd)//MP2/6- 311++G** or SAC-CI/6-31++G(3df,3pd)//MP2/6-311++G**), the general shape of the calculated UV/VIS spectral curves are quite similar for the lowest singlet states of ala- and galabenzene, and the same applies to the spectra of the normal modes. The calculated UV/VIS spectra of C5H5Al and C5H5Ga are featured by long wavelength bands of moderate intensity around 900 nm at the TD-DFT and between 1300 and 1500 nm at the SAC-CI level. According to both methods these bands are predominantly due to HOMO(π)→LUMO(σ*) transitions. The results of isodesmic bond separation reactions for the singlet states indicate some degree of stabilization due to delocalization in both of the title compounds. With our best values between 29 and 32 kcal/mol this stabilization appears to be only slightly less than the previously reported value for borabenzene (∼38 kcal/mol).

Structures of simple anions from ab initio molecular orbital calculations

1976 ◽  
Vol 29 (8) ◽  
pp. 1635 ◽  
Author(s):  
L Radom
Keyword(s):  
Ab Initio ◽  
Molecular Orbital ◽  
Basis Set ◽  
Basis Sets ◽  
Molecular Orbital Calculations ◽  
Limited Information ◽  
Orbital Theory ◽  
Comparable Quality ◽  
Split Valence ◽  
Theoretical Results

Ab initio molecular orbital theory with the minimal STO-3G and split-valence 4-31G basis sets is used to obtain geometries of 18 anions:OH-, NH2-, HF2-, BH4-, BF4-, C22-, CN-, NCN2-, N3-, NO2-, NO3-, 0CCO2-, CO32-, HCOO-, CH3COO-, C2O42-, C4O42- and C(CN)3-. The theoretical results are compared with experimental results from the literature. The STO-3G basis set performs somewhat worse for anions than for neutral molecules. On the other hand, the 4-31G basis set gives good results and predicts bond lengths to within 0.02� for all the molecules considered. Limited information on bond angle predictions suggests that these are of comparable quality to those for neutral molecules. The tricyanomethanide ion is predicted to be planar.

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