Copyright © 2002–2016 by A. Miyoshi
GPOP reference manual - gpop6irt

GPOP reference manual - gpop6irt


gpop6irt basename moi1 moi2


  gpop6irt simply calculates a reduced moment of inertia and a rotational constant for an intramolecular rotation, for pre-examination purpose. It reads a pre-processed GPOP-format file, basename.gpo, and prints output to standard output (or console, screen, display).   The intramolecular rotation is designated by the two moiety specifications on the command-line (moi1 and moi2).


  The molecular geometry is read from a GPOP-format file, basename.gpo.   The intramolecular roter is specified by two moiety-inputs as command line arguments.
Moiety input
  Each moiety if specified by a list of atoms. The first atom in the list must be the pivot atom for intramolecular rotation. The ordering of the indices is exactly the same as in the Gaussian output. For example;
gpop6irt iprR100 3-5-6-7 1-2-4-8-9-10
specifies intramolecular rotation around C[3]-C[1] bond of the isopropyl radical shown in the figure below.
The pivot carbon atom[3] must be the first atom in the moiety-1 and the counter pivot atom[1] must be the first atom in the moiety-2, while the ordering of the other atoms in each moiety is arbitrary. Because the counter moiety-2 usually contains all the other atoms that do not belong to moiety-1, the moiety-2 may be specified with the abbreviation mark '@', such as;
gpop6irt iprR100 3-5-6-7 1-@
Each moiety input can only contain numeric letters '0123456789' or hyphens '-', except that moiety-2 may contain '@' as the second atom.


  All the results are printed to the standard output (console).   Below, an output from,
gpop6irt iprR100 3-5-6-7 1-@
will be shown and explained.
First part: input confirmation
  The first part looks like,
base file name: iprR100
moiety-1: 3-5-6-7
moiety-2: 1-2-4-8-9-10
two moieties are whole molecule.
dihedral angle between moieties 1 and 2: -40.4044
First three lines merely repeat the command-line inputs, provided that the abbreviation mark '@' is explicitly expanded for moiety-2. The fourth line indicate whether the all atoms in the molecule is included in two moieties or not. The fifth and the last line of the first block indicates the dihedral angle between the plane including two pivots and the center of mass (c.o.m.) of moiety-1 and the plane including the pivots and c.o.m. of moiety-2. This information may be needed to define the angle of rotation.
Second part: main reports
  The second and the main part reports the reduced moments of inertia and corresponding rotational constants.
    appI[amuA2]: 3.15188566
    appB[cm-1]: 5.34842660
 --- symmetric top ---
 symRedI[amuA2]: 2.55256513
 symRedB[cm-1]: 6.60419157
 --- asymmetric top ---
 asmRedI[amuA2]: 2.55109775
 asmRedB[cm-1]: 6.60799027
    appI[amuA2]: 30.43526340
    appB[cm-1]: 0.55388478
 --- symmetric top ---
 symRedI[amuA2]: -25.44679284
 symRedB[cm-1]: -0.66246577
 --- asymmetric top ---
 asmRedI[amuA2]: 2.55109770
 asmRedB[cm-1]: 6.60799040
In many cases the result needed is the last --- asymmetric top --- part of the [moiety-1] output, either 'asmRedI[amuA2]' (the reduced moment inertia in aum Å2 unit) or 'asmRedB[cm-1]' (corresponding rotational constant in cm–1 unit). Other output are intermediate results or for diagnostic purpose. Briefly, the first part contains the apparent top moment of inertia (appI) and corresponding rotational constant (appB). The second --- symmetric top --- part containes reduced moment of inertia (symRedI) and rotational constant (symRedB) calculated by symmetric formula.
Third part: mode assignment
  The last part reports the similarity of the intramolecular rotation with the normal vibrational modes.
[most resembling vibrations]
 mode-001: 0.79846374
 mode-002: 0.59494241
 mode-008: 0.14970760
This may help to identify the corresponding vibrational mode. The similarity coefficient, the absolute figure of the dot product of vibrational mode vector and the internal rotation vector, is shown after the mode number.

Calculation details

Moment of inertia and rotational constant
  The calculations are done according to the Pitzer's protocols [1, 2]. The output appI is the top apparent moment of inertia around the axis, and is Am in Pitzer's definition. Thus, appB is the corresponding rotational constant. The 'symmetric top' section reports the symmetric top properties [1] and symRedI is the reduced moment of inertia of a symmetric top, Im, calculated by equation (1a) of [1], and accordingly, symRedB is corresponding rotational constant.
  The last section of each moiety output reports the results of asymmetric calculation [2]. asmRedI is the reduced moment of inertia calculated by equation (1) in [2]. Due to the symmetric formula, the calculation for moiety-1 and moiety-2 should be the same except for the minor numerical errors, provided when two moieties cover while atoms in the molecule.
Similarity to normal mode vibrations
  The program also investigates the similarity to the normal mode vibrations. The first-order deviation vector for internal mode (vibrational mode or intramolecular rotation) is defined by;
v = T(dx1, dy1, dz1, dx2, dy2, dz2, ... dxn, dyn, dzn)
where dxi, dyi, and dzi denote the deviation of x, y, and y coordinate of atom i. The similarity coefficient of mode-j (vj) to the intramolecular rotation (vIR) is defined as the absolute figure of the dot product;
Sj, IR = |vj ·vIR| / (|vj| |vIR|)
The program reports the top three most resembling vibrational modes with the similarity coefficients. If the highest similarity coefficient is significantly smaller than unity (1.0), the coupling between the intramolecular rotation and other vibration or internal rotation is suggested. The above example for isopropyl radical is this case. See reference manual for gpop6mrt for detail of this problem.


[1] K. S. Pitzer and W. D. Gwinn, J. Chem. Phys. 10, 428 (1942).
[2] K. S. Pitzer, J. Chem. Phys. 14, 239 (1946).