From acfc2417a9629956c2d93d9ba223aa201997cd9e Mon Sep 17 00:00:00 2001 From: Kirk C Pearce Date: Sun, 12 Jun 2022 13:30:03 -0400 Subject: [PATCH 1/8] 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 --- Project#01/README.md | 60 +++++++++++++++--- Project#01/figures/.DS_Store | Bin 8196 -> 0 bytes Project#01/figures/dark/bond-angle.png | Bin 0 -> 20201 bytes Project#01/figures/dark/center-of-mass.png | Bin 0 -> 51481 bytes Project#01/figures/dark/distances.png | Bin 0 -> 32935 bytes Project#01/figures/dark/inertia-diag.png | Bin 0 -> 51649 bytes Project#01/figures/dark/inertia-off-diag.png | Bin 0 -> 39619 bytes Project#01/figures/dark/oop-angle.png | Bin 0 -> 34703 bytes .../figures/dark/principal-mom-of-inertia.png | Bin 0 -> 13077 bytes Project#01/figures/dark/rot-const.png | Bin 0 -> 58586 bytes Project#01/figures/dark/torsion-angle.png | Bin 0 -> 40611 bytes Project#01/figures/dark/unit-vectors.png | Bin 0 -> 41706 bytes Project#01/figures/distances2.png | Bin 8117 -> 0 bytes 13 files changed, 50 insertions(+), 10 deletions(-) delete mode 100644 Project#01/figures/.DS_Store create mode 100644 Project#01/figures/dark/bond-angle.png create mode 100644 Project#01/figures/dark/center-of-mass.png create mode 100644 Project#01/figures/dark/distances.png create mode 100644 Project#01/figures/dark/inertia-diag.png create mode 100644 Project#01/figures/dark/inertia-off-diag.png create mode 100644 Project#01/figures/dark/oop-angle.png create mode 100644 Project#01/figures/dark/principal-mom-of-inertia.png create mode 100644 Project#01/figures/dark/rot-const.png create mode 100644 Project#01/figures/dark/torsion-angle.png create mode 100644 Project#01/figures/dark/unit-vectors.png delete mode 100644 Project#01/figures/distances2.png diff --git a/Project#01/README.md b/Project#01/README.md index b6a1d47..5741bb4 100644 --- a/Project#01/README.md +++ b/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: - + + + + + 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, φijk, between atoms i-j-k, where j is the central atom is given by: - + + + + + where the eij are unit vectors between the atoms, e.g., - + + + + + - [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 eij 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 θijkl for atom i out of the plane containing atoms j-k-l (with k as the central atom, connected to i) is given by: - + + + + + - [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 θi ## Step 5: Torsion/Dihedral Angles Calculate all possible torsional angles. For example, the torsional angle τijkl for the atom connectivity i-j-k-l is given by: - + + + + + 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: - + + + + + where mi 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: - + + + + + Off-diagonal (add a negative sign): - + + + + + Diagonalize the inertia tensor to obtain the principal moments of inertia: - + + + + + Report the moments of inertia in amu bohr2, amu Å2, and g cm2. @@ -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-1 and MHz: - + + + + + - [Solution](./hints/step8-solution.md) diff --git 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.../dark/diag-mass-weighted-hessian.png | Bin 0 -> 13808 bytes .../figures/dark/hessian-file-format.png | Bin 0 -> 43363 bytes Project#02/figures/dark/hessian.png | Bin 0 -> 23124 bytes .../figures/dark/mass-weighted-hessian.png | Bin 0 -> 24319 bytes Project#02/figures/dark/vib-freq.png | Bin 0 -> 22553 bytes .../figures/diag-mass-weighted-hessian.pdf | Bin 0 -> 59028 bytes Project#02/figures/hessian-file-format.pdf | Bin 0 -> 53943 bytes Project#02/figures/hessian.pdf | Bin 0 -> 60590 bytes Project#02/figures/mass-weighted-hessian.pdf | Bin 0 -> 52183 bytes Project#02/figures/vib-freq.pdf | Bin 0 -> 62972 bytes 12 files changed, 25 insertions(+), 5 deletions(-) delete mode 100644 Project#02/figures/.DS_Store create mode 100644 Project#02/figures/dark/diag-mass-weighted-hessian.png create mode 100644 Project#02/figures/dark/hessian-file-format.png create mode 100644 Project#02/figures/dark/hessian.png create mode 100644 Project#02/figures/dark/mass-weighted-hessian.png create mode 100644 Project#02/figures/dark/vib-freq.png create mode 100644 Project#02/figures/diag-mass-weighted-hessian.pdf create mode 100644 Project#02/figures/hessian-file-format.pdf create mode 100644 Project#02/figures/hessian.pdf create mode 100644 Project#02/figures/mass-weighted-hessian.pdf create mode 100644 Project#02/figures/vib-freq.pdf diff --git a/Project#02/README.md b/Project#02/README.md index 758b491..38dc35a 100644 --- a/Project#02/README.md +++ b/Project#02/README.md @@ -14,13 +14,21 @@ 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. - + + + + + The Hessian matrix (in units of Eh/a02) can be downloaded [here](./input/h2o_hessian.txt) for the H2O 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: - + + + + + * [Hint 1](./hints/hint1.md): Reading the Hessian @@ -28,7 +36,11 @@ while the remaining values have the following format: Divide each element of the Hessian matrix by the product of square-roots of the masses of the atoms associated with the given coordinates: - + + + + + where mi 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: - + + + + + 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). 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one can solve directly. 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