Introducing the coordinates in Z-matrix form. Objectives study how to introduce the coordinates of a molecule in Z-matrix form
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1 Introducing the coordinates in Z-matrix form Objectives study how to introduce the coordinates of a in Z-matrix form
2 The Z-matrix provides a description of each atom in a in terms of the internal coordinates Internal coordinates: Species of each atom Distances Angles Torsion (dihedral) angles This is particularly useful when working with molecular systems or restricted optimizations (control optimization variables) The name arises because the Z-matrix assigns the second atom along the Z-axis from the first atom, which is at the origin.
3 This specifies the atoms that make up each and their geometry.
4 In addition, an option may be passed, that indicates the units in which distances are specified in fractional scaled In the absence of such an option, the distance units are taken to be the value of ZM.UnitsLength
5 Nspecie i j k r a t ifr ifa ift One line per each atom in the Integers Double precision Integers
6 Nspecie i j k r a t ifr ifa ift One line per each atom in the Integers Double precision Species number of the atom Integer flags that indicate whether r, a, and t, respectively, should be varied in a relaxation or molecular dynamics ; 0 for fixed, 1 for varying.
7 The coordinates of the first atom the easiest one. It will be taken as the origin Nspecie Species number of the atom For the first atom, set them to 0 Cartesian coordinates (let us take as the origin in this example)
8 The coordinates of the second atom Nspecie Nspecie d Coordinates, in spherical coordinates, of the second atom with respect to the first atom In this particular example, this is just the distance along the z-axis of the second atom with respect to the first
9 The coordinates of the third atom Nspecie Nspecie d Nspecie d31 Distance of the third atom to the atom indicated in this position (in this example, this number indicates the distance between atom 3 and atom 1)
10 The coordinates of the third atom Nspecie Nspecie d Nspecie d31 a123 Angle made by the third atom with respect atoms indicated here and here (in this example, this number indicates the angle formed between atoms 1, 2, and 3)
11 The coordinates of the third atom Nspecie Nspecie d Nspecie d31 a123 t Torsional angle made by the third atom with respect atoms indicated here, here, and here (for the third atom is defined relative to a notional atom 1 unit in the z-direction above the atom j)
12 The rest of the atoms follow the same specification: Distance with respect atom i Angle with respect atom j and i Torsional angle with respect atoms k, j, and i Nspecie Nspecie d Nspecie d31 a123 t NspecieX. %endblock Zmatrix
13 Instead of specifying a numerical value, it is possible to specify a symbol within the above geometry definitions. Example, the water fractional HO HO2 HOH variables HO HO Define the symbol as variables constant HOH Define the symbol as a constant %endblock Zmatrix
14 Exercise: define the coordinates of a CH4 in Z-matrix form CH CH CH CH variables CH %endblock Zmatrix ZM.UnitsLength Ang ZM.UnitsAngle Deg Modify the distance CH by hand and find the equilibrium distance
15 Exercise: Compute the energy for different C-H bond lengths siesta < ch4.fdf > ch4.your_distance.ang.out In the present example, try from 1.05 to 1.30 Ang in steps of 0.05 Ang Modify this variable Tabulate the energy as a function of the C-H bond length grep Total = ch4.*.ang.out > ch4.distance.dat These numbers have been obtained with siesta-3.0-b, compiled with the g95 compiler and double precision in the grid. Numbers might change slightly depending on the platform, compiler and compilation flags
16 Exercise: Compute the energy for different C-H bond lengths gnuplot gnuplot> plot ch4.distance.dat using 1:2 with lines Compare the equilibrium distance with the experimental distance of 1.09 Å
17 Compute the equilibrium distance by means of a Conjugate Gradient minimization: Single-ζ basis set Edit the input file and introduce the following lines (this has been done for you in the ch4.cg.fdf file) siesta < ch4.cg.fdf > ch4.cg.out Search in the output file the relaxed structure Here you are the equilibrium distance
18 Compute the equilibrium distance by means of a Conjugate Gradient minimization: Double-ζ plus polarization basis set Edit the input file and change PAO.BasisSize to DZP (this has been done for you in the ch4.cg.dzp.fdf file) siesta < ch4.cg.dzp.fdf > ch4.cg.dzp.out Search in the output file the relaxed structure and compare with the experimental value of 1.09 Å
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