@@ -14,21 +14,33 @@ for the remainder of this project is the water molecule, optimized at the SCF/DZ
1414The primary input data for the harmonic vibrational calculation is the Hessian matrix,
1515which consists of second derivatives of the energy with respect to atomic positions.
1616
17- <img src =" ./figures/hessian.png " height =" 50 " >
17+ <picture >
18+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/hessian.png " >
19+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/hessian.png " >
20+ <img src =" ./figures/hessian.png " height =" 50 " >
21+ </picture >
1822
1923The 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.
2024The 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),
2125while the remaining values have the following format:
2226
23- <img src =" ./figures/hessian-file-format.png " width =" 200 " >
27+ <picture >
28+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/hessian-file-format.png " >
29+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/hessian-file-format.png " >
30+ <img src =" ./figures/hessian-file-format.png " width =" 200 " >
31+ </picture >
2432
2533 * [ Hint 1] ( ./hints/hint1.md ) : Reading the Hessian
2634
2735## Step 3: Mass-Weight the Hessian Matrix
2836
2937Divide each element of the Hessian matrix by the product of square-roots of the masses of the atoms associated with the given coordinates:
3038
31- <img src =" ./figures/mass-weighted-hessian.png " height =" 50 " >
39+ <picture >
40+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/mass-weighted-hessian.png " >
41+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/mass-weighted-hessian.png " >
42+ <img src =" ./figures/mass-weighted-hessian.png " height =" 50 " >
43+ </picture >
3244
3345where m<sub >i</sub > represents the mass of the atom corresponding to atom * i* . Use atomic mass units (amu) for the masses, just as
3446for [ Project #1 ] ( ../Project%2301 ) .
@@ -39,7 +51,11 @@ for [Project #1](../Project%2301).
3951
4052Compute the eigenvalues of the mass-weighted Hessian:
4153
42- <img src =" ./figures/diag-mass-weighted-hessian.png " height =" 20 " >
54+ <picture >
55+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/diag-mass-weighted-hessian.png " >
56+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/diag-mass-weighted-hessian.png " >
57+ <img src =" ./figures/diag-mass-weighted-hessian.png " height =" 20 " >
58+ </picture >
4359
4460You should consider using the same canned diagonalization function
4561you used in [ Project #1 ] ( ../Project%2301 ) .
@@ -50,7 +66,11 @@ you used in [Project #1](../Project%2301).
5066
5167The vibrational frequencies are proportional to the squareroot of the eigenvalues of the mass-weighted Hessian:
5268
53- <img src =" ./figures/vib-freq.png " height =" 25 " >
69+ <picture >
70+ <source media =" (prefers-color-scheme: dark) " srcset =" ./figures/dark/vib-freq.png " >
71+ <source media =" (prefers-color-scheme: light) " srcset =" ./figures/vib-freq.png " >
72+ <img src =" ./figures/vib-freq.png " height =" 25 " >
73+ </picture >
5474
5575The most common units to use for vibrational frequencies is cm<sup >-1</sup >.
5676
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