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This projects the wavefunction onto an **AGP** (Antisymmetrized Geminal Power) form **based on hybrid orbitals** rather than on atomic-orbital (AO) basis functions. You can visualize the generated hybrid orbitals with:
@@ -101,14 +104,16 @@ In the **Kekulé** picture of benzene, double and single bonds alternate around
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- 2–7, 12–17, 22–27 → **optimize** (set flag to ``1``)
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- 7–12, 17–22, 27–2 → **fixed to 0** (ensure value is 0 and set flag to ``-1``)
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- all the other indices → **optimize** (set flag to ``1``)
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Concretely, keep only the following **three** lines with flag ``1`` and set **all other** entries’ first column to ``-1``:
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Concretely, keep only the following **three** lines with flag ``-1`` and set **all other** entries’ first column to ``1``:
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.. code-block:: text
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1 2 7
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1 12 17
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1 22 27
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-1 2 27
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-1 7 12
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-1 17 22
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.. _turbogeniustutorial_9805_03:
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@@ -123,7 +128,7 @@ Once optimized, evaluate the energy with the optimized wavefunction:
@@ -288,14 +290,14 @@ Check the reblocked total energy and error in the file `pip0.d`.
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With both **Kekulé** and **resonating** AGP wavefunctions optimized and their energies computed, compare the two total energies to obtain a schematic measure of the stabilization due to aromatic resonance in benzene.
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- Kekule: -34.6293(75) Ha
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- Resonating: -34.7682(76) Ha
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- Kekule: -37.322... Ha
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- Resonating: -37.353... Ha
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.. tip::
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- Keep a clear record (e.g., a small table) of which :math:`\lambda` pairs are optimized vs. fixed for each case.
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- Verify that pairs set to zero in the Kekulé setup remain **exactly** zero during optimization (i.e., flagged ``-1``).
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- For reproducibility, retain the edited ``fort.10`` files (or diffs) in version control.
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- Since the hybrid orbitals used here are smaller than the basis sets used in :ref:`previous chapter <turbogeniustutorial_1001_10>`, the obtained energy with the resonating wavefunction is slightly worse.
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.. [#geo_ref] GEO hybrid-orbital construction reference: DOI: https://doi.org/10.1063/1.4938089
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