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Fix Project 1 transparent images
testing again test testing again Testing differences in old vs new image behavior .gitignore changes Replacing second equation testing Fix Project 1 transparent images Adding missed OOP img
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Project#01/README.md

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## Step 2: Bond Lengths
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Calculate the interatomic distances using the expression:
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<img src="./figures/distances.png" height="40">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/distances.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/distances.png">
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<img src="./figures/distances.png" height="40">
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</picture>
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where x, y, and z are Cartesian coordinates and i and j denote atomic indices.
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## Step 3: Bond Angles
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Calculate all possible bond angles. For example, the angle, &phi;<sub>ijk</sub>, between atoms i-j-k, where j is the central atom is given by:
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<img src="./figures/bond-angle.png" height="25">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/bond-angle.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/bond-angle.png">
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<img src="./figures/bond-angle.png" height="25">
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</picture>
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where the e<sub>ij</sub> are unit vectors between the atoms, e.g.,
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<img src="./figures/unit-vectors.png" height="30">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/unit-vectors.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/unit-vectors.png">
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<img src="./figures/unit-vectors.png" height="30">
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</picture>
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- [Hint 1](./hints/hint3-1.md): Memory allocation for the unit vectors
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- [Hint 2](./hints/hint3-2.md): Avoiding a divide-by-zero
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## Step 4: Out-of-Plane Angles
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Calculate all possible out-of-plane angles. For example, the angle &theta;<sub>ijkl</sub> for atom i out of the plane containing atoms j-k-l (with k as the central atom, connected to i) is given by:
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<img src="./figures/oop-angle.png" height="60">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/oop-angle.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/oop-angle.png">
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<img src="./figures/oop-angle.png" height="60">
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</picture>
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- [Hint 1](./hints/hint4-1.md): Memory allocation?
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- [Hint 2](./hints/hint4-2.md): Cross products
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## Step 5: Torsion/Dihedral Angles
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Calculate all possible torsional angles. For example, the torsional angle &tau;<sub>ijkl</sub> for the atom connectivity i-j-k-l is given by:
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<img src="./figures/torsion-angle.png" height="60">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/torsion-angle.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/torsion-angle.png">
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<img src="./figures/torsion-angle.png" height="60">
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</picture>
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Can you also determine the sign of the torsional angle?
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## Step 6: Center-of-Mass Translation
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Find the center of mass of the molecule:
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<img src="./figures/center-of-mass.png" width="600">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/center-of-mass.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/center-of-mass.png">
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<img src="./figures/center-of-mass.png" width="600">
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</picture>
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where m<sub>i</sub> is the mass of atom i and the summation runs over all atoms in the molecule.
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Diagonal:
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<img src="./figures/inertia-diag.png" width="750">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/inertia-diag.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/inertia-diag.png">
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<img src="./figures/inertia-diag.png" width="750">
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</picture>
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Off-diagonal (add a negative sign):
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<img src="./figures/inertia-off-diag.png" width="600">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/inertia-off-diag.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/inertia-off-diag.png">
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<img src="./figures/inertia-off-diag.png" width="600">
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</picture>
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Diagonalize the inertia tensor to obtain the principal moments of inertia:
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<img src="./figures/principal-mom-of-inertia.png" width="125">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/principal-mom-of-inertia.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/principal-mom-of-inertia.png">
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<img src="./figures/principal-mom-of-inertia.png" width="125">
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</picture>
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Report the moments of inertia in amu bohr<sup>2</sup>, amu &#8491;<sup>2</sup>, and g cm<sup>2</sup>.
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## Step 8: Rotational Constants
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Compute the rotational constants in cm<sup>-1</sup> and MHz:
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<img src="./figures/rot-const.png" width="100">
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<picture>
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<source media="(prefers-color-scheme: dark)" srcset="./figures/dark/rot-const.png">
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<source media="(prefers-color-scheme: light)" srcset="./figures/rot-const.png">
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<img src="./figures/rot-const.png" width="100">
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</picture>
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- [Solution](./hints/step8-solution.md)
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Project#01/figures/.DS_Store

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