Pushing the limit for the grid-based treatment of Schrödinger's equation: a sparse Numerov approach for one, two and three dimensional quantum problems

Literature Information

Publication Date 2016-10-20
DOI 10.1039/C6CP06698D
Impact Factor 3.676
Authors

Ulrich Kuenzer, Jan-Andrè Sorarù, Thomas S. Hofer


View Original

Abstract

The general Numerov method employed to numerically solve ordinary differential equations of second order was adapted with a special focus on solving Schrödinger's equation. By formulating a hierarchy of novel stencil expressions for the numerical treatment of the Laplace operator in one, two and three dimensions the method could not only be simplified over the standard Numerov scheme. The improved framework enables the natural use of matrix sparsity to reduce the memory demand and the associated computing time, thus enabling the application of the method to larger problems. The performance of the adapted method is demonstrated using exemplary harmonic and Morse problems in one and two dimensions. Furthermore, the vibrational frequencies of molecular hydrogen and water are calculated, inherently considering the influence of anharmonicity, mode–mode coupling and nuclear quantum effects. The estimation of the tunneling splitting in malonaldehyde serves as an example for a two-dimensional problem.

Related Literature

News & Views

Paper

DOI: 10.1039/B008754H

Teaching green chemistry: from lemons to lemonade bottles

2003-06-03 News

DOI: 10.1039/B305233H

Contents

Front/Back Matter

DOI: 10.1039/B0RP90008G

Diary of conferences and courses

Other

DOI: 10.1039/JA995100057N

Editorial

Paper

DOI: 10.1039/B100448O

Foreword

News

DOI: 10.1039/B202711A

News and Views

News

DOI: 10.1039/B206505N

You might also like

Compound Q&A

What are the main uses of (3.beta.)-3-Hydroxy-N,N-dimethyl-chol-5-en-24-amide (CAS: 79066-03-8)?

(3.beta.)-3-Hydroxy-N,N-dimethyl-chol-5-en-24-amide (CAS: 79066-03-8) is primari...

79066-03-8(3.beta.)-3-Hydroxy-...
Compound Q&A

What regulatory guidelines apply to 5-(aminomethyl)-2-methoxyphenol (CAS: 89702-89-6)?

5-(Aminomethyl)-2-methoxyphenol (CAS: 89702-89-6) is classified under GHS as a s...

89702-89-65-(aminomethyl)-2-me...
Compound Q&A

What is Thieno[2,3-c]pyridin-7(6H)-one (CAS: 28981-13-7)?

Thieno[2,3-c]pyridin-7(6H)-one (CAS: 28981-13-7) is a heterocyclic organic compo...

28981-13-7Thieno[2,3-c]pyridin...
Compound Q&A

Is 1-[(6-Methoxy-3-pyridinyl)methyl]-4-piperidinamine dihydrochloride (CAS: 1185311-28-7) safe?

1-[(6-Methoxy-3-pyridinyl)methyl]-4-piperidinamine dihydrochloride is generally ...

1185311-28-71-[(6-Methoxy-3-pyri...
Compound Q&A

What regulatory guidelines apply to [(2E)-3-Phenyl-2-propen-1-yl]phosphonic acid (CAS: 146404-58-2)?

[(2E)-3-Phenyl-2-propen-1-yl]phosphonic acid (CAS: 146404-58-2) is regulated und...

146404-58-2[(2E)-3-Phenyl-2-pro...
Compound Q&A

What regulatory guidelines apply to 6-Bromo-7-methoxyquinoline (CAS: 1620515-86-7)?

6-Bromo-7-methoxyquinoline (CAS: 1620515-86-7) falls under the scope of the Glob...

1620515-86-76-Bromo-7-methoxyqui...
Compound Q&A

What industries use (2R)-1-(1-Benzofuran-2-yl)-N-propyl-2-pentanamine (CAS: 260550-89-8)?

This compound is primarily used in the pharmaceutical industry for the developme...

260550-89-8(2R)-1-(1-Benzofuran...
1228013-15-71-Ethyl-7-[2-methyl-...
Compound Q&A

Are there alternatives to {5-(Acryloylamino)-2-[(dimethylamino)methyl]phenyl}boronic acid (CAS: 1217500-78-1) in synthesis?

Alternative reagents such as 2-[(dimethylamino)methyl]phenylboronic acid or rela...

1217500-78-1{5-(Acryloylamino)-2...
Compound Q&A

What is 3-(Piperidin-4-yloxy)pyridine (CAS: 310881-48-2)?

3-(Piperidin-4-yloxy)pyridine (CAS: 310881-48-2) is an organic compound with the...

310881-48-23-(Piperidin-4-yloxy...

Source Journal

Physical Chemistry Chemical Physics

Physical Chemistry Chemical Physics
CiteScore: 5.5
Self-citation Rate: 10.3%
Articles per Year: 3036

Physical Chemistry Chemical Physics (PCCP) is an international journal co-owned by 19 physical chemistry and physics societies from around the world. This journal publishes original, cutting-edge research in physical chemistry, chemical physics and biophysical chemistry. To be suitable for publication in PCCP, articles must include significant innovation and/or insight into physical chemistry; this is the most important criterion that reviewers and Editors will judge against when evaluating submissions. The journal has a broad scope and welcomes contributions spanning experiment, theory, computation and data science. Topical coverage includes spectroscopy, dynamics, kinetics, statistical mechanics, thermodynamics, electrochemistry, catalysis, surface science, quantum mechanics, quantum computing and machine learning. Interdisciplinary research areas such as polymers and soft matter, materials, nanoscience, energy, surfaces/interfaces, and biophysical chemistry are welcomed if they demonstrate significant innovation and/or insight into physical chemistry. Joined experimental/theoretical studies are particularly appreciated when complementary and based on up-to-date approaches.

Recommended Compounds

Recommended Suppliers

Disclaimer
This page provides academic journal information for reference and research purposes only. We are not affiliated with any journal publishers and do not handle publication submissions. For publication-related inquiries, please contact the respective journal publishers directly.
If you notice any inaccuracies in the information displayed, please contact us at support@chemtradehub.com. We will promptly review and address your concerns.