Copyright © 2002–2016 by A. Miyoshi

GPOP reference manual - gpop6mrt

GPOP reference manual - gpop6mrt

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GPOP reference manual - **gpop6mrt**

Synopsis

Description

`gpop6mrt`

calculates reduced moments of inertia and
rotational constants for multiple intramolecular rotations,
for pre-examination purpose. It reads a pre-processed GPOP-format
file, *basename*.gpo

, and multiple rotor specification
file, *basename*.mrt

, and prints output to standard
output.
This is a succeeding version of

`gpop6irt`

and it
calculates the reduced moments of inertia as well as the coupling
analysis of the intramolecular rotors. This treatment is still experimental
and has not been implemented in `gpop3tst`

and the tools which
use its output (`gpop4thf`

and `tstrate`

).
Input

The program expects following two input files in the current
directory.

1) | A GPOP-format file, . |

2) | An multiple internal rotor input file, . |

Internal Rotor Input in .mrt File

Following is the content of sample .mrt file,

`iprR100.mrt`

;1:3-5-6-7 1:4-8-9-10Each line corresponds to a internal rotor, with a format;

Thepivot-moi2:moi1

*moi1*

input is the same as that in
`gpop6irt`

program, while the moiety-2 is specified by the pivot atom only.
The sample input specifies the rotation around C[1]–C[3]
bond and that around C[1]–C[4] bond.
Extended Input in .mrt File

For the calculation of moment of inertia and rotational constant
of bending vibrations, the following optional input is accepted.
An example input is shown for the transition state of OH + benzene
H-abstraction reaction.

1:2-8-9 z1:2-8-9 x1:2-8-9 y1:2-8-9The first and the second lines are identical, and specifies a moiety consisting of H2, O8, and H9 rotating around C1-H2 axis. Here, the z-axis is defined by the two pivot atoms, C1 and H2. The x-axis is defined so as it pass through the center of mass of the moiety, and y-axis perpendicular to both z- and x- axes. The third line specifies the rotation around the axis parallel to x-axis and passing through the pivot, H2. In other words, this is a out of plane C1-H2-O8 bending (wagging). Similarly, the fourth line specifies the rotation around the axis parallel to y-axis and passing through the pivot, H2, or the C1-H2-O8 in-plane bending (rocking).

For more flexible specification of the rotation axis, following
two types of the extension are also available.**v-option:** The input beginning with 'v' specifies the
rotation axis direction by
the vector connecting two atoms specified after '|'. The first input
line above specifies the rocking vibration of H2-O8-H9 moiety.

**p-option:** The input beginning with 'p' specifies the
rotation axis by two vectors.
The second input line indicates the direction of the rotation axis is
both perpendicular to C3-C7 and C4-C6 vectors, that is, it corresponds
to the wagging vibarion of H2-O8-H9 moiety.
In this example,
the second type of input with 'p' is necessary to specify the wagging
vibration of the molecule deviated in the direction of wagging
coordinates, because the deviation changes the center of mass of the
moiety, and specification with 'x' is no longer the axis of wagging
vibration.

**i-option:** The 'i' option specifies the axes of rotation
by cartesian vector in the input geometry. The third line in above
example specifies the axis is cartesian (0,0,1) vector.

v1:2-8-9|3-4 p1:2-8-9|3-7:4-6 i1:2-8-9|0:0:1

Output

The results are printed to the standard output. Followings
are explanation of the example output from:
`gpop6mrt iprR100`

Single rotor properties

The first part reports the single rotor properties as;

----- Uncoupled Properties ----- ucR#1: I= 2.55110 B= 6.60799 1 (0.801) 2 (0.595) 8 (0.150) ucR#2: I= 2.55110 B= 6.60799 1 (0.801) 2 (0.595) 8 (0.150)which are same as those reported by

`gpop6irt`

but in
concise format.
Coupled rotor properties

The second part reports the properties of coupled rotors as;*ψ*_{1} =
(–*θ*_{1} + *θ*_{2})
/ 2^{1/2}
[*I*_{1} = 2.025 amu Å^{2}]

*ψ*_{2} = (*θ*_{1} +
*θ*_{2}) / 2^{1/2}
[*I*_{2} = 3.077 amu Å^{2}]
where *θ*_{i} denotes the coordinate of
*i*-th localized (input) rotation, *ψ*_{j}
is the *j*-th orthogonal coordinates, and *I*_{j}
is corresponding reduced moment of inertia. The most resembling vibrations
output indicates that the poor similarity coefficients for input
localized rotations are successfully improved by the appropriate
coupling calculation, that is, the vibrational mode #2 with frequency
128.193 cm^{–1} is assymetric internal rotation while
mode #1 with frequency 115.293 cm^{–1} is symmetric
internal rotation.

DSYEV info:0 lw-opt:68.000 ----- Coupling Calculation Results ----- cpR#1: I= 2.02510 B= 8.32433 vec= -0.707 0.707 cpR#2: I= 3.07709 B= 5.47843 vec= 0.707 0.707 ----- Coupled - most resembling vibrations ----- cpR#1: 2 (0.994) 8 (0.251) 3 (0.250) freq=128.193 cpR#2: 1 (1.000) 7 (0.042) 20 (0.025) freq=115.293The first line is a diagnostic message for DSYEV subroutine in LAPACK, which does not need to be care usually. The coupling calculation results show that the two input localized rotations couples with 1:1 ratio, and the resultant orthogonal roational coordinates and corresponding reduced moments of inertia are;

Diagnostic / decoupling output

The last section reports the results of decoupling.

----- diagnostic of coupling ----- ----- Decoupled Frequencies ----- ucR#1: 120.578 ucR#2: 120.578 ----- Partition Function Correction Factor ----- 0.979Decoupled frequencies are inversely calculated vibrational frequencies for uncoupled (localized) internal rotations. Because of the full symmetry of two local internal rotations, the results gave two identical frequencies for these two equivalent motion. The partition function correction factor must be used when calculating the partition function with localized approximation, and thus it is a measure of the strength of coupling.

Calculation details

The coupling calculations are done according to Kilpatrick and
Pitzer [3]. This coupling treatment has not yet
been implemented in the tools for thermodynamic or rate constant
calculations.

References

[3] | J. E. Kilpatrick and K. S. Pitzer, J. Chem. Phys. 17,
1064 (1949). |