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| CARTESIAN | The molecular structure is given in Cartesian coordinates. | ||
| ZMATRIX | The molecular structure is defined by a Z-matrix. The
form
Z-MATRIX is equivalent to ZMATRIX. | ||
| MIXED | The first atoms of the molecular structure are defined by Cartesian coordinates and the following ones are defined by a Z-matrix. |
| ANGSTROM | Coordinates or bond distances are given in Ångströms. | ||
| BOHR | Coordinates or bond distances are given in atomic units. |
O may be specified as:
GEOMETRY CARTESIAN ANGSTROM O 0.00 0.00 0.00 H 0.76 0.00 0.52 H -0.76 0.00 0.52
The Cartesian coordinates of an individual atom, defined by the atomic symbol (e.g. H2), or an atom group, defined by the element symbol (e.g. H), can be frozen during the geometry optimization in redundant coordinates. To keep all three degrees of freedom of an atom fixed the corresponding atomic symbol or element symbol has to be specified with the string XYZ in the keyword body of CONSTANTS. The string X will freeze only the x coordinate of the corresponding atom, the string XY fixes the x and y coordinates, etc. In the following example, the oxygen atom is kept frozen and the movements of all hydrogen atoms are restricted to the xz-plane (y coordinate frozen) during the optimization.
GEOMETRY CARTESIAN ANGSTROM O 0.00 0.00 0.00 H 0.76 0.00 0.52 H -0.76 0.00 0.52 # CONSTANTS O XYZ H Y
As usual, the comment line (#) is given only for clarity. The effective nuclear charge (in atomic units), which is identical to the number of electrons counted for the atom, and the nuclear mass (in atomic mass units; amu) can be specified by an integer and real number after the coordinates, respectively. Therefore, the following input for a water-like system consists of a frozen oxygen atom, a hydrogen atom, H1, fixed in the xz-plane with the effective nuclear charge 0, i.e. a ghost atom that can be used to define basis functions at a point in space, and another hydrogen atom, H2, with the nuclear charge 1 and the nuclear mass 2.014, i.e. a deuterium atom.
GEOMETRY CARTESIAN ANGSTROM O 0.00 0.00 0.00 H1 0.76 0.00 0.52 0 H2 -0.76 0.00 0.52 1 2.014 # CONSTANTS O XYZ H1 Y
If quantities are not specified, default values are used (e.g. the O atom in the example above has a nuclear charge of 8 and a mass of 15.999 amu).
Negative integer numbers after the atomic coordinates indicate an MM atom. The absolute value of this integer number specifies the atom type in the selected force field. These atom types can be found in the FFDS file. Thus, the geometry part of an MM water input can have the form:
GEOMETRY CARTESIAN ANGSTROM O 0.00 0.00 0.00 -76 H1 0.76 0.00 0.52 -77 H2 -0.76 0.00 0.52 -77
Here 76 and 77 are the atom types of the MM oxygen and hydrogen atoms, respectively. Note that the connectivity between the atoms is generated automatically. The following input shows the geometry definition of a QM/MM water dimer, the first one being QM and the second one being MM.
GEOMETRY CARTESIAN ANGSTROM O 1.159094 0.359472 -1.228183 8 15.999400 H 0.165274 0.461227 -1.247218 1 1.007940 H 1.357609 -0.118689 -2.058595 1 1.007940 O -1.496793 0.620303 -1.289943 -76 H -2.123457 0.067624 -0.732608 -77 H -1.996365 1.430082 -1.611984 -77
For the QM atoms the nuclear charges and masses are also explicitly defined in this input. Again the connectivity of the MM atoms is generated automatically.
Even though it is usually advantageous to sort a QM/MM geometry definition according to the QM and MM atoms, this is not mandatory for a deMon2k input. In the following input QM and MM atoms are mixed among themselves. Note also the extended element symbols. This naming must be chosen such that the first two characters remain specific for the element. Thus, Hm and Hq used below are possible choices for hydrogen whereas He or Ho would denote helium or holmium, respectively!
GEOMETRY CARTESIAN ANGSTROM Hm1b 1.262389 -1.937796 1.222724 -77 6 Hq1a 0.217713 0.505507 -1.369657 Hm1a 1.124357 -0.596134 0.419304 -77 6 Hq1b 1.503324 -0.129952 -1.999029 Oq2 -1.628323 0.600651 -1.413703 Om1 0.867185 -1.043515 1.275905 -76 1 3 Hq2a -1.885969 0.153697 -0.557057 Om2 -1.948708 -0.776469 1.058175 -76 10 12 Hq2b -2.021673 1.495719 -1.360149 Hm2a -0.978710 -0.948944 1.231841 -77 8 Oq1 1.187632 0.332759 -1.195914 Hm2b -2.264749 -0.314968 1.861890 -77 8
In this input the integer numbers after the negative atom type specifications of the MM atoms denote their connectivity. Thus, hydrogen atom Hm1b and Hm1a are connected to atom 6 which is the MM oxygen atom Om1. For this atom two connectivity integer numbers are given, 1 and 3, that indicate the connectivities to atom 1, Hm1b, and atom 3, Hm1a.
If the geometry of the system is given by a Z-matrix, using the option ZMATRIX, each line in the keyword body of GEOMETRY describes the connectivity of the atom, which again is defined by its atomic symbol. The first atom (A) of the Z-matrix defines the origin of the input (see Figure 2) and therefore has no connectivity information.
The second atom (B) lies on the z-axis of the input coordinate system and is connected to the first atom at a distance RAB. The third atom (C) lies in the xz-plane and connects to the two previously defined atoms at a distance RBC and an angle TABC. Each of the following atoms is defined by an input line in free format containing the information:
LABEL NB RAB NC TABC ND PABCD
Here LABEL is the atomic label of atom A. NB, NC, and ND are the Z-matrix line numbers or the atomic labels of the atoms B, C and D with respect to which atom A is defined by a length (RAB), angle (TABC), and dihedral angle (PABCD). These are the so-called internal coordinates of the system. Their values are given by RAB (in Ångström or Bohr), TABC, and PABCD (in degrees), respectively. The maximum length of these numbers in the Z-matrix is limited to ten characters. The dihedral angle is defined by the angle between the planes spanned by the atoms {A, B, C} and {B, C, D}, respectively. The sign of the dihedral angle is defined according to the Newman projection shown in Figure 3. If the projection angle is oriented clockwise then the dihedral angle is positive.
Instead of giving the values for RAB, TABC, and PABCD directly in the Z-matrix,
they may also be represented by symbolic strings with no more than eight
characters each. These strings must be assigned to CONSTANT or VARIABLE values
(see 4.1.3 and 4.1.5) in the input, as the following example
of the C
H
input demonstrates:
GEOMETRY ZMATRIX ANGSTROM C1 C2 C1 rCC H1 C1 rCH C2 aCCH H2 C1 rCH C2 aCCH H1 dHCCH H3 C2 rCH C1 aCCH H2 dHCCH H4 C2 rCH C1 aCCH H1 dHCCH # VARIABLES rCC 1.3390 rCH 1.0850 aCCH 121.09 # CONSTANT dHCCH 180.0
The internal coordinates listed under VARIABLES are changed during geometry optimization, whereas the coordinates listed under CONSTANTS are kept frozen. The RAB, TABC, and PABCD values that are directly defined in the Z-matrix are always interpreted as constants in internal or internal redundant structure optimizations.
If one uses internal coordinates, dummy atoms are often useful. The atomic symbol X has been reserved for them (note that the symbol XX is reserved for automatically generated dummy atoms; it is not to be processed as an input symbol). The following example shows the use of a dummy atom in the definition of HCN.
GEOMETRY ZMATRIX ANGSTROM H C 1 R1 X 2 1.0 1 90.0 N 2 R2 3 A1 1 180.0 # VARIABLES R1 1.089 R3 1.166 A1 90.00
Here the dummy atom is used to avoid a 180
angle which might cause
problems in a geometry optimization. Please note that the structure parameters
which are defined inside the Z-matrix are kept constant during structure
optimization. Example ![[*]](crossref.png)
on page of the deMon2k
tutorial shows the use of a dummy atom for the definition of a ring system.
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To facilitate the input of the internal coordinates,
substitutions of angles and dihedral angles are possible in the Z-matrix input.
The substitutions are indicated by strings after the connectivity information
in each Z-matrix line. The possible substitution strings are listed in Table
4. Thus, the connectivity information in a Z-matrix line
can be extended by the substitution string, the nuclear charge, and the atomic
mass, respectively. This ordering is necessary! However, defaults can be omitted.
That is, the definition of a substitution string and an atomic mass will
work and the default nuclear charge will be assigned to the given atom. The examples
and on page and page
of the tutorial show some common applications of Z-matrix inputs.
If the geometry of the system is given by a MIXED input, the first few atoms are defined by Cartesian coordinates. At least the first three atoms, including dummy atoms, must be defined in this way. Subsequent atoms can then be defined by a Z-matrix line as described above. The reference atoms in that Z-matrix line can be defined either by Cartesian or internal coordinates. In either case, the coordinate system orientation is defined by the first three atoms. The following example, depicted in Figure 4, shows a MIXED input for a CO molecule adsorbed on a MgO cluster.
GEOMETRY MIXED ANGSTROM Mg1 0.000 0.000 0.000 O2 0.000 2.105 0.000 O3 2.105 0.000 0.000 O4 0.000 -2.105 0.000 O5 -2.105 0.000 0.000 Mg6 2.105 2.105 0.000 Mg7 2.105 -2.105 0.000 Mg8 -2.105 -2.105 0.000 Mg9 -2.105 2.105 0.000 O10 0.000 0.000 -2.105 Mg11 0.000 2.105 -2.105 Mg12 2.105 0.000 -2.105 Mg13 0.000 -2.105 -2.105 Mg14 -2.105 0.000 -2.105 O15 2.105 2.105 -2.105 O16 2.105 -2.105 -2.105 O17 -2.105 -2.105 -2.105 O18 -2.105 2.105 -2.105 C19 Mg1 RAD O2 AAD O3 DAD X20 C19 1.0 Mg1 90.0 O2 180.0 O21 C19 RCO X20 90.0 Mg1 180.0 # CONSTANTS Mg XYZ O2 XYZ O3 XYZ O4 XYZ O5 XYZ O10 XYZ O15 XYZ O16 XYZ O17 XYZ O18 XYZ # VARIABLES RAD 2.0 AAD 90.0 DAD 90.0 RCO 1.4
This example calls for the free optimization of a CO molecule, including internal relaxation, on a frozen MgO cluster surface. Thus, the MgO cluster is kept constant by freezing its Cartesian coordinates (see 4.1.3). The carbon atom of the CO molecule is defined with respect to the Mg1, O2, and O3 atoms of the cluster (see Figure 4) through the internal coordinates RAD, AAD, and DAD. These coordinates are free for optimization because they are declared as variables (see 4.1.5). The same holds for the CO bond length that is defined by the internal coordinate RCO. The dummy atom X20 must be used to avoid an ill-defined dihedral angle if the O21, C, Mg1 arrangement becomes linear.
In deMon2k Z-MATRIX and MIXED geometry definitions are also available for MM
and QM/MM calculations. Note that the dummy atom line in the following Z-matrix
definition for an MM input has to be taken into account for the MM connectivity
numbering.
GEOMETRY Z-MATRIX ANGSTROM O -76 15.999400 2 3 H 1 R1 -77 1.007940 1 H 1 R2 2 A1 RAD -77 1.007940 1 H 1 R3 2 A2 3 D1 RAD -77 1.007940 6 X1 4 RCON 1 ACON 2 DCON RAD 0 0.000000 O 4 R4 5 A3 1 D2 RAD -76 15.999400 4 7 H 6 R5 4 A4 5 D3 RAD -77 1.007940 6 # VARIABLES R1 1.00275988 R2 1.00278094 R3 1.72377877 R4 1.01622488 R5 0.99833459 A1 108.809982 A2 122.743681 A3 86.814590 A4 108.264348 D1 -152.130713 D2 181.980680 D3 33.280793 # CONSTANTS RCON 2.00000000 ACON 90.000000 DCON -138.000000
![\includegraphics[width=8.0cm]{/home/gerald/guide.5.0/Figures.5.0/ZMATRIX.eps}](ug-img65.png)
![\includegraphics[width=12.0cm]{/home/gerald/guide.5.0/Figures.5.0/DIHEDRAL.eps}](ug-img66.png)
![\includegraphics[width=11.0cm]{/home/gerald/guide.5.0/Figures.5.0/MIXED.eps}](ug-img70.png)