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GPOP reference manual - gpop6irt

GPOP reference manual - gpop6irt

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GPOP reference manual - **gpop6irt**

Synopsis

Description

`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*

).
Input

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 '`gpop6irt iprR100 3-5-6-7 1-@`
Each moiety input can only contain numeric letters
'

`@`

', such as;
`0123456789`

' or hyphens '`-`

', except that
moiety-2 may contain '`@`

' as the second atom.
Output

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: -40.4044First 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.^{2} unit) or '^{–1} unit).
Other output are intermediate results or for diagnostic purpose.
Briefly, the first part contains the apparent top moment of inertia
(

[moiety-1] 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 [moiety-2] 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]: 6.60799040In 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 Å`asmRedB[cm-1]`

'
(corresponding rotational constant in cm`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.*similarity coefficient*,
the absolute figure of the dot product of vibrational mode vector and
the internal rotation vector, is shown after the mode number.

[most resembling vibrations] mode-001: 0.79846374 mode-002: 0.59494241 mode-008: 0.14970760This may help to identify the corresponding vibrational mode. The

Calculation details

Moment of inertia and rotational constant

The calculations are done according to the Pitzer's protocols
[1, 2]. The output
*apparent* moment of inertia around
the axis, and is *A*_{m} in Pitzer's definition. Thus,
*I*_{m}, calculated by equation (1a) of
[1], and accordingly,

`appI`

is the top `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,
`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}(d*x*_{1}, d*y*_{1}, d*z*_{1},
d*x*_{2}, d*y*_{2}, d*z*_{2}, ...
d*x*_{n}, d*y*_{n}, d*z*_{n})
where d*x*_{i}, d*y*_{i}, and
d*z*_{i} denote the deviation of *x*, *y*, and *y*
coordinate of atom *i*. The similarity coefficient of mode-*j*
(**v**_{j}) to the intramolecular rotation (**v**_{IR})
is defined as the absolute figure of the dot product;
*S*_{j, IR} = |**v**_{j}
·**v**_{IR}| / (|**v**_{j}|
|**v**_{IR}|)
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.
References

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

[2] | K. S. Pitzer, J. Chem. Phys. 14, 239 (1946). |