Full Optical Rotation Tensor at CCSD Level in the Modified Velocity Gauge

2020 ◽  
Author(s):  
Kaihua Zhang ◽  
Ty Balduf ◽  
Marco Caricato
Keyword(s):  
Electric Dipole ◽  
Optical Rotation ◽  
Electric Quadrupole ◽  
Polarizability Tensor ◽  
Dipole Polarizability ◽  
Difficult Case ◽  
Computationally Efficient ◽  
Rotation Tensor ◽  
Approximate Methods ◽  
Velocity Gauge

<div> <div> <p> </p><div> <div> <div> <p>This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10-20% with CAM-B3LYP and 20-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(–)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistently with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials. </p> </div> </div> </div> </div> </div>

Solution of heat and mass transfer problems with non-linear coefficients

2019 ◽  
Vol 5 (4) ◽  
pp. 10-20
Author(s):  
Boris G. Aksenov ◽  
Yuri E. Karyakin ◽  
Svetlana V. Karyakina
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Numerical Methods ◽  
Heat And Mass Transfer ◽  
Unknown Function ◽  
Comparison Theorems ◽  
Upper And Lower Bounds ◽  
Maximum Deviation ◽  
Approximate Methods ◽  
Nonmonotonic Dependence

Equations, which have nonlinear nonmonotonic dependence of one of the coefficients on an unknown function, can describe processes of heat and mass transfer. As a rule, existing approximate methods do not provide solutions with acceptable accuracy. Numerical methods do not involve obtaining an analytical expression for the unknown function and require studying the convergence of the algorithm used. The value of absolute error is uncertain. The authors propose an approximate method for solving such problems based on Westphal comparison theorems. The comparison theorems allow finding upper and lower bounds of the unknown exact solution. A special procedure developed for the stepwise improvement of these bounds provide solutions with a given accuracy. There are only a few problems for equations with nonlinear nonmonotonic coefficients for which the exact solution has been obtained. One of such problems, presented in this article, shows the efficiency of the proposed method. The results prove that the proposed method for obtaining bounds of the solution of a nonlinear nonmonotonic equation of parabolic type can be considered as a new method of the approximate analytical solution having guaranteed accuracy. In addition, the proposed here method allows calculating the maximum deviation from the unknown exact solution of the results of other approximate and numerical methods.

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

scholarly journals Helium Isotopes Quantum Sieving through Graphtriyne Membranes

Nanomaterials ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 73
Author(s):  
Marta I. Hernández ◽  
Massimiliano Bartolomei ◽  
José Campos-Martínez
Keyword(s):  
Low Temperatures ◽  
Quantum Tunneling ◽  
Transition State Theory ◽  
Selective Adsorption ◽  
State Theory ◽  
Helium Isotopes ◽  
Quantum Calculations ◽  
Approximate Methods ◽  
Helium Atoms ◽  
Quantum Behavior

We report accurate quantum calculations of the sieving of Helium atoms by two-dimensional (2D) graphtriyne layers with a new interaction potential. Thermal rate constants and permeances in an ample temperature range are computed and compared for both Helium isotopes. With a pore larger than graphdiyne, the most common member of the γ-graphyne family, it could be expected that the appearance of quantum effects were more limited. We find, however, a strong quantum behavior that can be attributed to the presence of selective adsorption resonances, with a pronounced effect in the low temperature regime. This effect leads to the appearance of some selectivity at very low temperatures and the possibility for the heavier isotope to cross the membrane more efficiently than the lighter, contrarily to what happened with graphdiyne membranes, where the sieving at low energy is predominantly ruled by quantum tunneling. The use of more approximate methods could be not advisable in these situations and prototypical transition state theory treatments might lead to large errors.

scholarly journals Reduction of the molecular hamiltonian matrix using quantum community detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Susan M. Mniszewski ◽  
Pavel A. Dub ◽  
Sergei Tretiak ◽  
Petr M. Anisimov ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Community Detection ◽  
Slater Determinant ◽  
Hamiltonian Matrix ◽  
Approximate Methods ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Molecular Hamiltonian ◽  
Structure Problem ◽  
Modularity Maximization ◽  
Chemical Knowledge

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

c. Internal rotation of the nitroso group in p-substituted nitrosoanilines by the density matrix line-shape method

1974 ◽  
Vol 27 (1) ◽  
pp. 21 ◽  
Author(s):  
PD Buckley ◽  
AR Furness ◽  
KW Jolley ◽  
DN Pinder
Keyword(s):  
Density Matrix ◽  
Internal Rotation ◽  
Line Shape ◽  
Matrix Theory ◽  
Activation Parameters ◽  
Nitroso Group ◽  
Approximate Methods ◽  
Density Matrix Theory

Density matrix theory has been applied to study the barrier to internal rotation about the Ar-NO bond in N,N-dimethyl-p-nitrosoaniline and N,N-diethyl-p-nitrosoaniline. Theoretical fits to experimental n.m.r. spectra have been obtained in the range - 30°C to +40°C. Activation parameters have been determined and compared with those obtained by more approximate methods.

scholarly journals An evolutionary approach to the vehicle route planning in e-waste mobile collection on demand

2021 ◽  
Vol 25 (8) ◽  
pp. 6665-6680
Author(s):  
Krzysztof Szwarc ◽  
Piotr Nowakowski ◽  
Urszula Boryczka
Keyword(s):  
Tabu Search ◽  
Quality Evaluation ◽  
Memetic Algorithm ◽  
Route Planning ◽  
Memetic Algorithms ◽  
Approximate Methods ◽  
On Demand ◽  
Suboptimal Solutions ◽  
Novel Method ◽  
The Given

AbstractThe article discusses the utilitarian problem of the mobile collection of waste electrical and electronic equipment. Due to its $$\mathcal {NP}$$ NP -hard nature, implies the application of approximate methods to discover suboptimal solutions in an acceptable time. The paper presents the proposal of a novel method of designing the Evolutionary and Memetic Algorithms, which determine favorable route plans. The recommended methods are determined using quality evaluation indicators for the techniques applied herein, subject to the limits characterizing the given company. The proposed Memetic Algorithm with Tabu Search provides much better results than the metaheuristics described in the available literature.

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

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