@@ -27,7 +27,11 @@ After downloading the file to your computer (to a file called “geom.dat”, fo
2727## Step 2: Bond Lengths
2828Calculate the interatomic distances using the expression:
2929
30- <img src =" ./figures/distances.png " height =" 40 " >
30+ <picture >
31+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/distances.png " >
32+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/distances.png " >
33+ <img src =" ./figures/distances.png " height =" 40 " >
34+ </picture >
3135
3236where x, y, and z are Cartesian coordinates and i and j denote atomic indices.
3337
@@ -40,11 +44,19 @@ where x, y, and z are Cartesian coordinates and i and j denote atomic indices.
4044## Step 3: Bond Angles
4145Calculate 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:
4246
43- <img src =" ./figures/bond-angle.png " height =" 25 " >
47+ <picture >
48+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/bond-angle.png " >
49+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/bond-angle.png " >
50+ <img src =" ./figures/bond-angle.png " height =" 25 " >
51+ </picture >
4452
4553where the e<sub >ij</sub > are unit vectors between the atoms, e.g.,
4654
47- <img src =" ./figures/unit-vectors.png " height =" 30 " >
55+ <picture >
56+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/unit-vectors.png " >
57+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/unit-vectors.png " >
58+ <img src =" ./figures/unit-vectors.png " height =" 30 " >
59+ </picture >
4860
4961- [ Hint 1] ( ./hints/hint3-1.md ) : Memory allocation for the unit vectors
5062- [ 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.,
5668## Step 4: Out-of-Plane Angles
5769Calculate 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:
5870
59- <img src =" ./figures/oop-angle.png " height =" 60 " >
71+ <picture >
72+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/oop-angle.png " >
73+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/oop-angle.png " >
74+ <img src =" ./figures/oop-angle.png " height =" 60 " >
75+ </picture >
6076
6177- [ Hint 1] ( ./hints/hint4-1.md ) : Memory allocation?
6278- [ Hint 2] ( ./hints/hint4-2.md ) : Cross products
@@ -67,7 +83,11 @@ Calculate all possible out-of-plane angles. For example, the angle θ<sub>i
6783## Step 5: Torsion/Dihedral Angles
6884Calculate all possible torsional angles. For example, the torsional angle &tau ; <sub >ijkl</sub > for the atom connectivity i-j-k-l is given by:
6985
70- <img src =" ./figures/torsion-angle.png " height =" 60 " >
86+ <picture >
87+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/torsion-angle.png " >
88+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/torsion-angle.png " >
89+ <img src =" ./figures/torsion-angle.png " height =" 60 " >
90+ </picture >
7191
7292Can you also determine the sign of the torsional angle?
7393
@@ -80,7 +100,11 @@ Can you also determine the sign of the torsional angle?
80100## Step 6: Center-of-Mass Translation
81101Find the center of mass of the molecule:
82102
83- <img src =" ./figures/center-of-mass.png " width =" 600 " >
103+ <picture >
104+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/center-of-mass.png " >
105+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/center-of-mass.png " >
106+ <img src =" ./figures/center-of-mass.png " width =" 600 " >
107+ </picture >
84108
85109where m<sub >i</sub > is the mass of atom i and the summation runs over all atoms in the molecule.
86110
@@ -95,15 +119,27 @@ Calculate elements of the [moment of inertia tensor](http://en.wikipedia.org/wik
95119
96120Diagonal:
97121
98- <img src =" ./figures/inertia-diag.png " width =" 750 " >
122+ <picture >
123+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/inertia-diag.png " >
124+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/inertia-diag.png " >
125+ <img src =" ./figures/inertia-diag.png " width =" 750 " >
126+ </picture >
99127
100128Off-diagonal (add a negative sign):
101129
102- <img src =" ./figures/inertia-off-diag.png " width =" 600 " >
130+ <picture >
131+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/inertia-off-diag.png " >
132+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/inertia-off-diag.png " >
133+ <img src =" ./figures/inertia-off-diag.png " width =" 600 " >
134+ </picture >
103135
104136Diagonalize the inertia tensor to obtain the principal moments of inertia:
105137
106- <img src =" ./figures/principal-mom-of-inertia.png " width =" 125 " >
138+ <picture >
139+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/principal-mom-of-inertia.png " >
140+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/principal-mom-of-inertia.png " >
141+ <img src =" ./figures/principal-mom-of-inertia.png " width =" 125 " >
142+ </picture >
107143
108144Report the moments of inertia in amu bohr<sup >2</sup >, amu Å ; <sup >2</sup >, and g cm<sup >2</sup >.
109145
@@ -116,7 +152,11 @@ Based on the relative values of the principal moments, determine the [molecular
116152## Step 8: Rotational Constants
117153Compute the rotational constants in cm<sup >-1</sup > and MHz:
118154
119- <img src =" ./figures/rot-const.png " width =" 100 " >
155+ <picture >
156+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/rot-const.png " >
157+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/rot-const.png " >
158+ <img src =" ./figures/rot-const.png " width =" 100 " >
159+ </picture >
120160
121161- [ Solution] ( ./hints/step8-solution.md )
122162
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