How do the Hückel and Baird Rules Fade away in Annulenes?
Abstract
:1. Introduction
2. Methodology
2.1. Aromaticity Indices
2.1.1. The Aromatic Fluctuation Index: FLU
2.1.2. The Bond-Length and Bond-Order Alternation Indices
2.1.3. A Many-Center Electron Delocalization Index:
2.1.4. AV1245 and
2.2. Hückel Molecular Orbital Method
3. Results
3.1. Aromaticity from the HMO Method
3.2. Geometrical Relaxation
3.2.1. Annulenes
3.2.2. Annulenes
3.3. Aromaticity from DFAs
3.4. The Delocalization Error in DFAs
4. Materials and Methods
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
AOM | Atomic overlaps matrix |
AV1245 | Aromaticity index for large rings [55] |
Minimal value of 12-45 delocalizations [56] | |
BLA | Bond-length alternation |
BOA | Bond-order alternation |
DFA | Density Functional Approximation |
DI | Delocalization index [28] |
FLU | Fluctuation aromaticity index [27] |
HF | Hartree-Fock |
HMO | Hückel Molecular Orbital |
HOMA | Harmonic Oscillator Model of Aromaticity [33] |
LDA | Local density approximation [109] |
MCI | Multicenter index [43] |
RE | Resonance energy |
TREPE | Topological resonance energy per electron |
Giambiagi’s multicenter index [42] | |
Approximation to (Equation (8)) |
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Structure | Multiplicity | Functional | FLU | 1/N | BOA | BLA | 1/N | | | |
---|---|---|---|---|---|---|---|---|
CH | S | HF | 0.000 | 0.624 | 0.000 | 0.000 | 0.597 | 10.25 |
B3LYP | 0.000 | 0.625 | 0.000 | 0.000 | 0.603 | 10.72 | ||
CAM-B3LYP | 0.000 | 0.628 | 0.000 | 0.000 | 0.603 | 10.71 | ||
M06-2X | 0.000 | 0.626 | 0.000 | 0.000 | 0.603 | 10.73 | ||
CH | T | HF | 0.024 | 0.393 | 0.246 | 0.089 | 0.341 | 0.39 |
B3LYP | 0.025 | 0.399 | 0.275 | 0.090 | 0.353 | 1.51 | ||
CAM-B3LYP | 0.025 | 0.408 | 0.276 | 0.091 | 0.363 | 1.20 | ||
M06-2X | 0.041 | 0.467 | 0.281 | 0.056 | 0.380 | 0.28 | ||
CH (twist) | S | HF | 0.068 | 0.421 | 0.728 | 0.157 | 0.339 | 0.00 |
B3LYP | 0.052 | 0.480 | 0.639 | 0.128 | 0.322 | 0.03 | ||
CAM-B3LYP | 0.059 | 0.466 | 0.677 | 0.137 | 0.341 | 0.03 | ||
M06-2X | 0.058 | 0.463 | 0.670 | 0.136 | 0.325 | 0.05 | ||
CH (heart) | S | HF | 0.065 | 0.436 | 0.712 | 0.153 | 0.380 | 0.01 |
B3LYP | 0.000 | 0.610 | 0.007 | 0.009 | 0.579 | 5.19 | ||
CAM-B3LYP | 0.000 | 0.614 | 0.009 | 0.010 | 0.579 | 5.13 | ||
M06-2X | 0.000 | 0.611 | 0.010 | 0.010 | 0.579 | 5.11 | ||
CH (naphthalene) | T | HF | 0.030 | 0.470 | 0.364 | 0.085 | 0.353 | 0.14 |
B3LYP | 0.023 | 0.531 | 0.328 | 0.064 | 0.460 | 0.91 | ||
CAM-B3LYP | 0.027 | 0.524 | 0.364 | 0.072 | 0.446 | 0.68 | ||
M06-2X | 0.028 | 0.522 | 0.367 | 0.073 | 0.444 | 0.63 | ||
CH (twist) | T | HF | 0.020 | 0.478 | 0.266 | 0.068 | 0.295 | 0.05 |
B3LYP | 0.020 | 0.517 | 0.305 | 0.066 | 0.352 | 0.08 | ||
CAM-B3LYP | 0.022 | 0.513 | 0.324 | 0.071 | 0.347 | 0.07 | ||
M06-2X | 0.022 | 0.511 | 0.328 | 0.072 | 0.337 | 0.10 | ||
CH | S | HF | 0.050 | 0.497 | 0.626 | 0.136 | - | 0.49 |
B3LYP | 0.001 | 0.605 | 0.010 | 0.008 | - | 4.24 | ||
CAM-B3LYP | 0.026 | 0.561 | 0.449 | 0.091 | - | 1.80 | ||
M06-2X | 0.025 | 0.561 | 0.438 | 0.088 | - | 1.89 | ||
CH (TS) | S | CAM-B3LYP | 0.000 | 0.609 | 0.007 | 0.007 | - | 4.29 |
M06-2X | 0.001 | 0.606 | 0.007 | 0.007 | - | 4.27 | ||
CH | T | HF | 0.021 | 0.502 | 0.282 | 0.069 | - | 0.01 |
B3LYP | 0.017 | 0.554 | 0.302 | 0.060 | - | 0.13 | ||
CAM-B3LYP | 0.023 | 0.544 | 0.348 | 0.071 | - | 0.08 | ||
M06-2X | 0.022 | 0.544 | 0.349 | 0.071 | - | 0.04 | ||
CH | S | HF | 0.049 | 0.504 | 0.616 | 0.133 | 0.472 | 0.57 |
B3LYP | 0.001 | 0.606 | 0.026 | 0.011 | 0.573 | 4.27 | ||
CAM-B3LYP | 0.026 | 0.563 | 0.446 | 0.090 | 0.530 | 1.80 | ||
M06-2X | 0.025 | 0.561 | 0.444 | 0.089 | 0.529 | 1.81 | ||
CH (TS) | S | CAM-B3LYP | 0.001 | 0.609 | 0.022 | 0.010 | 0.572 | 4.29 |
M06-2X | 0.001 | 0.607 | 0.022 | 0.010 | 0.572 | 4.28 | ||
CH | T | HF | 0.018 | 0.514 | 0.257 | 0.060 | 0.411 | 0.12 |
B3LYP | 0.013 | 0.570 | 0.265 | 0.053 | 0.533 | 0.58 | ||
CAM-B3LYP | 0.019 | 0.559 | 0.324 | 0.066 | 0.513 | 0.30 | ||
M06-2X | 0.019 | 0.559 | 0.324 | 0.065 | 0.517 | 0.46 |
Structure | Multiplicity | Method | FLU | 1/N | BOA | BLA | 1/N | | | |
---|---|---|---|---|---|---|---|---|
CH | S | HF | 0.101 | 0.391 | 0.888 | 0.249 | 0.262 | - |
B3LYP | 0.104 | 0.416 | 0.900 | 0.247 | 0.266 | - | ||
CAM-B3LYP | 0.103 | 0.398 | 0.898 | 0.245 | 0.264 | - | ||
M06-2X | 0.103 | 0.405 | 0.898 | 0.242 | 0.268 | - | ||
CH | T | HF | 0.010 | 0.507 | 0.000 | 0.000 | 0.433 | - |
B3LYP | 0.012 | 0.499 | 0.000 | 0.000 | 0.440 | - | ||
CAM-B3LYP | 0.011 | 0.504 | 0.000 | 0.000 | 0.439 | - | ||
M06-2X | 0.011 | 0.505 | 0.000 | 0.000 | 0.438 | - | ||
CH | S | HF | 0.067 | 0.436 | 0.726 | 0.156 | 0.406 | 0.30 |
B3LYP | 0.056 | 0.477 | 0.664 | 0.134 | 0.441 | 0.72 | ||
CAM-B3LYP | 0.061 | 0.468 | 0.693 | 0.140 | 0.428 | 0.52 | ||
M06-2X | 0.062 | 0.460 | 0.694 | 0.141 | 0.427 | 0.51 | ||
CH | T | HF | 0.001 | 0.590 | 0.000 | 0.000 | 0.534 | 4.07 |
B3LYP | 0.001 | 0.589 | 0.000 | 0.000 | 0.540 | 4.31 | ||
CAM-B3LYP | 0.001 | 0.593 | 0.000 | 0.000 | 0.539 | 4.29 | ||
M06-2X | 0.001 | 0.591 | 0.000 | 0.000 | 0.539 | 4.29 | ||
CH | S | HF | 0.063 | 0.445 | 0.698 | 0.153 | - | 0.04 |
B3LYP | 0.042 | 0.511 | 0.565 | 0.115 | - | 0.01 | ||
CAM-B3LYP | 0.050 | 0.494 | 0.624 | 0.128 | - | 0.02 | ||
M06-2X | 0.050 | 0.488 | 0.624 | 0.128 | - | 0.06 | ||
CH | T | HF | 0.021 | 0.487 | 0.280 | 0.067 | - | 0.07 |
B3LYP | 0.002 | 0.590 | 0.033 | 0.012 | - | 0.07 | ||
CAM-B3LYP | 0.015 | 0.562 | 0.288 | 0.056 | - | 0.21 | ||
M06-2X | 0.008 | 0.577 | 0.208 | 0.039 | - | 0.13 | ||
CH (S) | S | HF | 0.054 | 0.486 | 0.651 | 0.139 | 0.440 | 0.33 |
B3LYP | 0.029 | 0.551 | 0.476 | 0.095 | 0.513 | 0.96 | ||
CAM-B3LYP | 0.041 | 0.529 | 0.564 | 0.113 | 0.484 | 0.64 | ||
M06-2X | 0.040 | 0.526 | 0.562 | 0.113 | 0.484 | 0.63 | ||
CH (C) | S | HF | 0.053 | 0.488 | 0.643 | 0.139 | 0.452 | 0.25 |
B3LYP | 0.029 | 0.548 | 0.474 | 0.096 | 0.512 | 0.78 | ||
CAM-B3LYP | 0.040 | 0.530 | 0.555 | 0.113 | 0.487 | 0.55 | ||
M06-2X | 0.039 | 0.526 | 0.553 | 0.112 | 0.487 | 0.58 | ||
CH (C) | T | HF | 0.001 | 0.598 | 0.013 | 0.005 | - | 1.08 |
B3LYP | 0.002 | 0.596 | 0.057 | 0.013 | - | 1.16 | ||
CAM-B3LYP | 0.015 | 0.568 | 0.294 | 0.059 | - | 0.35 | ||
M06-2X | 0.011 | 0.576 | 0.252 | 0.050 | - | 0.74 |
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Casademont-Reig, I.; Ramos-Cordoba, E.; Torrent-Sucarrat, M.; Matito, E. How do the Hückel and Baird Rules Fade away in Annulenes? Molecules 2020, 25, 711. https://doi.org/10.3390/molecules25030711
Casademont-Reig I, Ramos-Cordoba E, Torrent-Sucarrat M, Matito E. How do the Hückel and Baird Rules Fade away in Annulenes? Molecules. 2020; 25(3):711. https://doi.org/10.3390/molecules25030711
Chicago/Turabian StyleCasademont-Reig, Irene, Eloy Ramos-Cordoba, Miquel Torrent-Sucarrat, and Eduard Matito. 2020. "How do the Hückel and Baird Rules Fade away in Annulenes?" Molecules 25, no. 3: 711. https://doi.org/10.3390/molecules25030711