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Notes&Credits
This is not part of the official documentation of TINKER program package, but have been ideated by me for this wiki. If you do use these tutorials, please give
credit to Chembytes and spread the word. You are welcome to improve the tutorial, and,
if you do it, please consider to help me improve Chembytes and send me your tutorial or become member of Chembytes and write it yourself. Don't worry, you will be properly acknowledged for your work.
Intro
In this tutorial you will learn how to work with internal coordinates using
as test case the simple ethane molecule, CH3-CH3.
Some TINKER programs, such optirot, minrot, pssrot, etc., work with internal
coordinates. Internal coordinates express the relation between atoms in
a molecules in terms of atom connectivity, distances, angles and torsional
angles. As opposite, Cartesian coordinates define the molecules in terms of
the atomic positions. When a structure is given in internal coordinates,
we can also say that its z-matrix is given.
Editing the file ethane.int, you will see the following z-matrix:
8 Ethane
1 C 1
2 C 1 1 1.60000
3 H 5 1 1.10000 2 109.4700
4 H 5 1 1.10000 2 109.4700 3 109.4700 1
5 H 5 1 1.10000 2 109.4700 3 109.4700 -1
6 H 5 2 1.10000 1 109.4700 3 10.0000 0
7 H 5 2 1.10000 1 109.4700 6 109.4700 1
8 H 5 2 1.10000 1 109.4700 6 109.4700 -1
The z-matrix should be red as following:
- The first line, says that there are eight atoms in the system, and that the name of the molecule is Ethane.
- Second line set the origin of the system, i.e., from which atom start to build the molecule: first atom is atom 1, which is a carbon atom, C, and its atom type for the MM3 force field (see file ethane.key) is 1.
- Third line says that the second atom in the molecule is a carbon atom, C, having MM3's atom type 1, bonded to atom 1 placed at a distance of 1.6 Angstroms from the atom 1.
- Fourth line says that the third atom in the structure is an hydrogen atoms, H, having MM3's atom type 5, bonded to atom 1, placed at a distance of 1.1 Angstroms from atom 1 and forming an angle of 109.47 degrees with atom 2.
- Fifth line says that the fourth atom in the structure is an hydrogen atoms, H, having MM3's atom type 5, bonded to atom 1, placed at a distance of 1.1 Angstroms from atom 1, and forming an angle of 109.47 degrees with atom 2. Also, the dihedral angles between the planes defined by atoms 1 2 3 and 2 3 4 is 109.47 degrees. The last column indicates the chirality flag (to be honest I have never found this number in any other z-matrix, like those used in gaussian). The structure of this line is then repeated for all the remain atoms.
Z-matrices are particularly useful for conformational search, allowing to vary the geometry
of the molecules changing bonds, angles or torsional angles in a systematic way wondering to
rewrite the atomic coordinates for each geometry. As example, think to to sample the torsion
of the two methyl groups in the ethane with respect the central bond. you can easily change
the dihedral angles in the z-matrix, rather than write many cartesian coordinate files.
PART I: Internal coordinates Vs. Cartesian Coordinates
Internal coordinates, cannot be analyzed with analyze, nor it is possible to use them for
molecular dynamics, therefore you need to convert the structure in cartesian coordinates.
This can be easily done as following:
[user@desktop]$ intxyz ethane.int -k ethane.key
the file ethane.xyz should now be created, containing the coordinates of the atoms. This file can
be analyzed and optimize as you saw in tutorial 01. Also, it can be used to run molecular
dynamic simulations.
If for any reason, you need to convert a structure from cartesian coordinates into internal
coordinates, you can use TINKER xyzint program:
[user@desktop]$ xyzint ethane.xyz -k ethane.key
In order to the z-matrix, you are asked to choose between the
following modes:
Template (T), Dihedrals (D), Manual (M) or Automatic [A]
The automatic mode (default choice) should be fine. If you have
tried to convert the file ethane.xyz obtained before, you will find
a new file, ethane.int_2, which contains almost the same z-matrix you
had in the original ethane.int file.
PART II: Manipulate internal coordinates
You can get information about atoms or modify the z-matrix using intedit
[user@desktop]$ intedit ethane.int -k ethane.key
You should get the following message:
if a single atom number is entered, the current definition of
the atom will be displayed.
If two atom numbers are entered, the output gives the distance
between the atoms, and asks for a new bond length if applicable;
Entry of three atoms shows the angle, and entry of four atoms
will display the corresponding dihedral angle.
To change the chirality at an atom, enter its number and -1.
To change the type of an atom, enter its number, -1, and the
new atom type number.
A carriage return at the prompt will display the atom last
changed or the next atom after the one just examined.
Typing SHOW will display the contents of the current Z-matrix.
Entering EXIT writes a new file then stops, while QUIT aborts.
Try the different options to get familiar with this program. For example try to deform the
molecule and save it as ethane_deformed.int: this can come in handy to illustrate the
next part of the tutorial: the minimization.
PART III: optimize structures in internal coordinates
As told before, different optimization algorithms can be used to minimize a structure
using internal coordinates: mirot, optirot, pssrot and newtrot, the equivalent of
minimize, optimize, pss and newton for cartesian coordinates. You can try to optimize
the structures you have created before using intedit. With respect the cases studied in
the previous tutorial, these programs will prompt you the following message:
Selection of Torsional Angles for Rotation :
0 - Automatic Selection of Torsional Angles
1 - Manual Selection of Angles to Rotate
2 - Manual Selection of Angles to Freeze
Enter the Method of Choice [0] :
to know how to work with the rotational angles. All the other parameters required, should be the same as for the cartesian counterparts.
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