Computational quantum mechanics and the basis set problem

2006 ◽  
pp. 326-334
Author(s):  
C. L. Davis ◽  
H. -J. Aa. Jensen ◽  
H. J. Monkhorst
Keyword(s):  
Quantum Mechanics ◽  
Basis Set ◽  
Computational Quantum

scholarly journals Mechanism and origins of selectivity in the enantioselective oxa-Pictet–Spengler reaction: a cooperative catalytic complex from a hydrogen bond donor and chiral phosphoric acid

2020 ◽  
Vol 11 (33) ◽  
pp. 8736-8743
Author(s):  
Mark A. Maskeri ◽  
Alexander C. Brueckner ◽  
Taisiia Feoktistova ◽  
Matthew J. O'Connor ◽  
Daniel M. Walden ◽  
...  
Keyword(s):  
Hydrogen Bond ◽  
Quantum Mechanics ◽  
Phosphoric Acid ◽  
Catalytic Complex ◽  
Hydrogen Bond Donor ◽  
New Model ◽  
Chiral Phosphoric Acid ◽  
Computational Quantum

A new model for the cooperative catalytic oxa-Pictet–Spengler reaction is disclosed. Supporting spectroscopic, kinetic, and computational quantum mechanics studies permit the rationalization of the reaction's observed enantioselectivity.

Computational Quantum Mechanics

2018 ◽  
Author(s):  
Joshua Izaac ◽  
Jingbo Wang
Keyword(s):  
Quantum Mechanics ◽  
Computational Quantum

scholarly journals Current Developments in the Relativistic Quantum Mechanics of Atoms and Molecules

1986 ◽  
Vol 39 (5) ◽  
pp. 649 ◽  
Author(s):  
IP Grant
Keyword(s):  
Electronic Structure ◽  
Quantum Mechanics ◽  
Atomic Structure ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Finite Basis ◽  
Basis Set ◽  
Structure Theory ◽  
Relativistic Quantum Mechanics ◽  
Atoms And Molecules

Current work in relativistic quantum mechanics by the author and his associates focusses on four topics: atomic structure theory using the GRASP package (Dyall 1986); extension of GRASP to handle electron continuum processes; the relation of quantum electrodynamics and relativistic quantum mechanics of atoms and molecules; and development of methods using finite basis set expansions for studying electronic structure of atoms and molecules. This paper covers only the last three topics, giving emphasis to growing points and outstanding difficulties.

scholarly journals Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019 ◽  
Vol 34 (14) ◽  
pp. 1950107 ◽  
Author(s):  
V. H. Badalov ◽  
B. Baris ◽  
K. Uzun
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Basis Set ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions

The formal framework for quantum mechanics is an infinite number of dimensional space. Hereby, in any analytical calculation of the quantum system, the energy eigenvalues and corresponding wave functions can be represented easily in a finite-dimensional basis set. In this work, the approximate analytical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood–Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are derived for any angular momentum case by means of state-of-the-art Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transforming each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well [Formula: see text] and [Formula: see text], the radial [Formula: see text] and [Formula: see text] orbital quantum numbers and parameters [Formula: see text], [Formula: see text], [Formula: see text] are also identified in detail. Next, the bound state energies and corresponding normalized hyper-radial wave functions for the neutron system of the [Formula: see text]Fe nucleus are calculated in [Formula: see text] and [Formula: see text] as well as the energy spectrum expressions of other higher dimensions are revealed by using the energy spectrum of [Formula: see text] and [Formula: see text].

Basis set methods for describing the quantum mechanics of a ‘‘system’’ interacting with a harmonic bath

1987 ◽  
Vol 86 (3) ◽  
pp. 1451-1457 ◽  
Author(s):  
Nancy Makri ◽  
William H. Miller
Keyword(s):  
Quantum Mechanics ◽  
Basis Set ◽  
Harmonic Bath

Computational quantum mechanics: An underutilized tool in thermodynamics

2007 ◽  
Vol 79 (8) ◽  
pp. 1345-1359 ◽  
Author(s):  
Stanley I. Sandler ◽  
Marcelo Castier
Keyword(s):  
Quantum Mechanics ◽  
Continuum Solvation ◽  
Solvation Models ◽  
Computational Quantum

In this paper, we highlight the various ways computational quantum mechanics (QM) can be used in applied thermodynamics. We start with the most rigorous procedures of calculating the interactions between molecules that can then be used in simulation and progress, in steps, to less rigorous but easily used methods, including the very successful continuum solvation models.

scholarly journals Spectral methods in computational quantum mechanics

1991 ◽  
Vol 37 (1-3) ◽  
pp. 209-219 ◽  
Author(s):  
P. Maraner ◽  
E. Onofri ◽  
G.P. Tecchioli
Keyword(s):  
Quantum Mechanics ◽  
Spectral Methods ◽  
Computational Quantum

Implementation of atomic basis set composed of 1s Gaussian and 1s Slater-type orbitals to carry out quantum mechanics molecular calculations

1999 ◽  
Vol 20 (6) ◽  
pp. 604-609 ◽  
Author(s):  
J. C. Cesco ◽  
C. C. Denner ◽  
G. O. Giubergia ◽  
A. E. Rosso ◽  
J. E. P�rez ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Basis Set ◽  
Slater Type Orbitals ◽  
Slater Type ◽  
Molecular Calculations
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