Fix transparent equations

Project#01/README.md

@@ -27,7 +27,11 @@ After downloading the file to your computer (to a file called “geom.dat”, fo
 ## Step 2: Bond Lengths
 Calculate the interatomic distances using the expression:
 
-<img src="./figures/distances.png" height="40">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/distances.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/distances.png">
+  <img src="./figures/distances.png" height="40">
+</picture>
 
 where x, y, and z are Cartesian coordinates and i and j denote atomic indices.
 
@@ -40,11 +44,19 @@ where x, y, and z are Cartesian coordinates and i and j denote atomic indices.
 ## Step 3: Bond Angles
 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:
 
-<img src="./figures/bond-angle.png" height="25">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/bond-angle.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/bond-angle.png">
+  <img src="./figures/bond-angle.png" height="25">
+</picture>
 
 where the e<sub>ij</sub> are unit vectors between the atoms, e.g.,
 
-<img src="./figures/unit-vectors.png" height="30">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/unit-vectors.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/unit-vectors.png">
+  <img src="./figures/unit-vectors.png" height="30">
+</picture>
 
 - [Hint 1](./hints/hint3-1.md): Memory allocation for the unit vectors
 - [Hint 2](./hints/hint3-2.md): Avoiding a divide-by-zero
@@ -56,7 +68,11 @@ where the e<sub>ij</sub> are unit vectors between the atoms, e.g.,
 ## Step 4: Out-of-Plane Angles
 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:
 
-<img src="./figures/oop-angle.png" height="60">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/oop-angle.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/oop-angle.png">
+  <img src="./figures/oop-angle.png" height="60">
+</picture>
 
 - [Hint 1](./hints/hint4-1.md): Memory allocation?
 - [Hint 2](./hints/hint4-2.md): Cross products
@@ -67,7 +83,11 @@ Calculate all possible out-of-plane angles. For example, the angle &theta;<sub>i
 ## Step 5: Torsion/Dihedral Angles
 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:
 
-<img src="./figures/torsion-angle.png" height="60">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/torsion-angle.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/torsion-angle.png">
+  <img src="./figures/torsion-angle.png" height="60">
+</picture>
 
 Can you also determine the sign of the torsional angle?
 
@@ -80,7 +100,11 @@ Can you also determine the sign of the torsional angle?
 ## Step 6: Center-of-Mass Translation
 Find the center of mass of the molecule:
 
-<img src="./figures/center-of-mass.png" width="600">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/center-of-mass.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/center-of-mass.png">
+  <img src="./figures/center-of-mass.png" width="600">
+</picture>
 
 where m<sub>i</sub> is the mass of atom i and the summation runs over all atoms in the molecule.
 
@@ -95,15 +119,27 @@ Calculate elements of the [moment of inertia tensor](http://en.wikipedia.org/wik
 
 Diagonal:
 
-<img src="./figures/inertia-diag.png" width="750">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/inertia-diag.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/inertia-diag.png">
+  <img src="./figures/inertia-diag.png" width="750">
+</picture>
 
 Off-diagonal (add a negative sign):
 
-<img src="./figures/inertia-off-diag.png" width="600">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/inertia-off-diag.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/inertia-off-diag.png">
+  <img src="./figures/inertia-off-diag.png" width="600">
+</picture>
 
 Diagonalize the inertia tensor to obtain the principal moments of inertia:
 
-<img src="./figures/principal-mom-of-inertia.png" width="125">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/principal-mom-of-inertia.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/principal-mom-of-inertia.png">
+  <img src="./figures/principal-mom-of-inertia.png" width="125">
+</picture>
 
 Report the moments of inertia in amu bohr<sup>2</sup>, amu &#8491;<sup>2</sup>, and g cm<sup>2</sup>.
 
@@ -116,7 +152,11 @@ Based on the relative values of the principal moments, determine the [molecular
 ## Step 8: Rotational Constants
 Compute the rotational constants in cm<sup>-1</sup> and MHz:
 
-<img src="./figures/rot-const.png" width="100">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/rot-const.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/rot-const.png">
+  <img src="./figures/rot-const.png" width="100">
+</picture>
 
 - [Solution](./hints/step8-solution.md)
 

Project#01/hints/hint7-1.md

@@ -3,7 +3,11 @@ Here are two approaches for the [diagonalization](http://en.wikipedia.org/wiki/D
 ## Secular Determinant
 Since the moment of inertia tensor is only a 3x3 matrix, a brute-force approach via the secular determinant is feasible:
 
-<img src="../figures/determinant.png" height="60">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="../figures/dark/determinant.png">
+  <source media="(prefers-color-scheme: light)" srcset="../figures/determinant.png">
+  <img src="../figures/determinant.png" height="60">
+</picture>
 
 This leads to a cubic equation in &lambda;, which one can solve directly.  Have fun with that.
 

Project#02/README.md

@@ -14,21 +14,33 @@ for the remainder of this project is the water molecule, optimized at the SCF/DZ
 The primary input data for the harmonic vibrational calculation is the Hessian matrix,
 which consists of second derivatives of the energy with respect to atomic positions.
 
-<img src="./figures/hessian.png" height="50">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/hessian.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/hessian.png">
+  <img src="./figures/hessian.png" height="50">
+</picture>
 
 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. 
 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), 
 while the remaining values have the following format:
 
-<img src="./figures/hessian-file-format.png" width="200">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/hessian-file-format.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/hessian-file-format.png">
+  <img src="./figures/hessian-file-format.png" width="200">
+</picture>
 
  * [Hint 1](./hints/hint1.md): Reading the Hessian
 
 ## Step 3: Mass-Weight the Hessian Matrix
 
 Divide each element of the Hessian matrix by the product of square-roots of the masses of the atoms associated with the given coordinates:
 
-<img src="./figures/mass-weighted-hessian.png" height="50">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/mass-weighted-hessian.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/mass-weighted-hessian.png">
+  <img src="./figures/mass-weighted-hessian.png" height="50">
+</picture>
 
 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 
 for [Project #1](../Project%2301).
@@ -39,7 +51,11 @@ for [Project #1](../Project%2301).
 
 Compute the eigenvalues of the mass-weighted Hessian:
 
-<img src="./figures/diag-mass-weighted-hessian.png" height="20">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/diag-mass-weighted-hessian.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/diag-mass-weighted-hessian.png">
+  <img src="./figures/diag-mass-weighted-hessian.png" height="20">
+</picture>
 
 You should consider using the same canned diagonalization function 
 you used in [Project #1](../Project%2301).
@@ -50,7 +66,11 @@ you used in [Project #1](../Project%2301).
 
 The vibrational frequencies are proportional to the squareroot of the eigenvalues of the mass-weighted Hessian:
 
-<img src="./figures/vib-freq.png" height="25">
+<picture>
+  <source media="(prefers-color-scheme: dark)" srcset="./figures/dark/vib-freq.png">
+  <source media="(prefers-color-scheme: light)" srcset="./figures/vib-freq.png">
+  <img src="./figures/vib-freq.png" height="25">
+</picture>
 
 The most common units to use for vibrational frequencies is cm<sup>-1</sup>.