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Fix Project 2 transparent images
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Project#02/README.md

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@@ -14,21 +14,33 @@ for the remainder of this project is the water molecule, optimized at the SCF/DZ
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The primary input data for the harmonic vibrational calculation is the Hessian matrix,
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which consists of second derivatives of the energy with respect to atomic positions.
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<img src="./figures/hessian.png" height="50">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/hessian.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/hessian.png">
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<img src="./figures/hessian.png" height="50">
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</picture>
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The Hessian matrix (in units of E<sub>h</sub>/a<sub>0</sub><sup>2</sup>) can be downloaded [here](./input/h2o_hessian.txt) for the H<sub>2</sub>O test case.
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The first integer in the file is the number of atoms (which you should compare to the corresponding value from the geometry file as a test of consistency),
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while the remaining values have the following format:
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<img src="./figures/hessian-file-format.png" width="200">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/hessian-file-format.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/hessian-file-format.png">
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<img src="./figures/hessian-file-format.png" width="200">
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</picture>
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* [Hint 1](./hints/hint1.md): Reading the Hessian
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## Step 3: Mass-Weight the Hessian Matrix
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Divide each element of the Hessian matrix by the product of square-roots of the masses of the atoms associated with the given coordinates:
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<img src="./figures/mass-weighted-hessian.png" height="50">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/mass-weighted-hessian.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/mass-weighted-hessian.png">
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<img src="./figures/mass-weighted-hessian.png" height="50">
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</picture>
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where m<sub>i</sub> represents the mass of the atom corresponding to atom *i*. Use atomic mass units (amu) for the masses, just as
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for [Project #1](../Project%2301).
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Compute the eigenvalues of the mass-weighted Hessian:
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<img src="./figures/diag-mass-weighted-hessian.png" height="20">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/diag-mass-weighted-hessian.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/diag-mass-weighted-hessian.png">
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<img src="./figures/diag-mass-weighted-hessian.png" height="20">
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</picture>
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You should consider using the same canned diagonalization function
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you used in [Project #1](../Project%2301).
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The vibrational frequencies are proportional to the squareroot of the eigenvalues of the mass-weighted Hessian:
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<img src="./figures/vib-freq.png" height="25">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/vib-freq.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/vib-freq.png">
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<img src="./figures/vib-freq.png" height="25">
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</picture>
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The most common units to use for vibrational frequencies is cm<sup>-1</sup>.
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Project#02/figures/.DS_Store

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Project#02/figures/hessian.pdf

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