Copyright © 2002–2016 by A. Miyoshi
GPOP reference manual - gpop6mrt

GPOP reference manual - gpop6mrt


gpop6mrt basename


  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).


  The program expects following two input files in the current directory.
1) A GPOP-format file, basename.gpo.
2) An multiple internal rotor input file, basename.mrt.
Internal Rotor Input in .mrt File
  Following is the content of sample .mrt file, iprR100.mrt;
Each line corresponds to a internal rotor, with a format;
The 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.
The 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.


  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;
 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=115.293
The 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;
ψ1 = (–θ1 + θ2) / 21/2   [I1 = 2.025 amu Å2]
ψ2 = (θ1 + θ2) / 21/2   [I2 = 3.077 amu Å2]
where θi denotes the coordinate of i-th localized (input) rotation, ψj is the j-th orthogonal coordinates, and Ij 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.
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 -----
Decoupled 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.


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