Topological Analysis of Magnetically Induced Current Densities in Strong Magnetic Fields Using Stagnation Graphs
Abstract
:1. Introduction
2. Theoretical Background
2.1. Magnetically Induced Current Densities
2.2. Topological Characteristics
3. Computational Methods
3.1. Selecting an Appropriate Objective Function
3.2. Optimization Algorithm
Algorithm 1 Trust Region optimization |
|
3.3. Initial Point Selection
4. Results
4.1. CH
4.2. CH
4.3. CH
5. Discussion
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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i | Conditions | Magnetotropicity | Classification | |
---|---|---|---|---|
isolated singularity: saddle | ||||
isolated singularity: paramagnetic focus | ||||
isolated singularity: diamagnetic focus | ||||
stagnation line: saddle | ||||
stagnation line: paramagnetic vortex | ||||
stagnation line: diamagnetic vortex | ||||
branching point |
/ | Energy / | R / bohr | ∢ H–C–H / Degree | Point Group |
---|---|---|---|---|
0.00 | −40.541554 | 2.0638 | 109.5 | T |
0.05 | −40.536608 | 2.0631, 2.0632 | 109.4, 109.5 | C |
0.10 | −40.522124 | 2.0614, 2.0615 | 109.3, 109.6 | C |
0.15 | −40.499129 | 2.0585, 2.0604 | 109.2, 109.8 | C |
0.20 | −40.469243 | 2.0543, 2.0620 | 108.9, 110.0 | C |
/ | Energy / | R / bohr | R / bohr | ∢ H–C–C / Degree | Point Group |
---|---|---|---|---|---|
0.00 | −77.374420 | 2.2727 | 2.0136 | 180.0 | D |
0.05 | −77.368853 | 2.2722 | 2.0123 | 180.0 | C |
0.10 | −77.352224 | 2.2703 | 2.0085 | 180.0 | C |
0.15 | −77.378285 | 2.5974 | 2.0679 | 118.5 | C |
0.20 | −77.421742 | 2.6106 | 2.0658 | 115.8 | C |
/ | Energy / | R / bohr | R / bohr | ∢ H–C–H / Degree | Point Group |
---|---|---|---|---|---|
0.00 | −78.633815 | 2.5150 | 2.0532 | 116.5 | D |
0.05 | −78.628954 | 2.5146 | 2.0523 | 116.2 | C |
0.10 | −78.614244 | 2.5133 | 2.0497 | 115.2 | C |
0.15 | −78.589425 | 2.5110 | 2.0457 | 113.7 | C |
0.20 | −78.554391 | 2.5084 | 2.0407 | 111.5 | C |
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Irons, T.J.P.; Garner, A.; Teale, A.M. Topological Analysis of Magnetically Induced Current Densities in Strong Magnetic Fields Using Stagnation Graphs. Chemistry 2021, 3, 916-934. https://doi.org/10.3390/chemistry3030067
Irons TJP, Garner A, Teale AM. Topological Analysis of Magnetically Induced Current Densities in Strong Magnetic Fields Using Stagnation Graphs. Chemistry. 2021; 3(3):916-934. https://doi.org/10.3390/chemistry3030067
Chicago/Turabian StyleIrons, Tom J. P., Adam Garner, and Andrew M. Teale. 2021. "Topological Analysis of Magnetically Induced Current Densities in Strong Magnetic Fields Using Stagnation Graphs" Chemistry 3, no. 3: 916-934. https://doi.org/10.3390/chemistry3030067