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triat_U3_min User's Guide
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triat_U3_min User's Guide
triat_U3_min?
The Fortran programs in the triat_U3_min suite make
calculation making use of the two dimensional limit of the Vibron model. This
approach is used to model the bending dynamics of linear, quasilinear and bent
molecules, using an algebraic model based on a bosonic U(3) Lie algebra. This
suite includes several programs, working with a fourteen parameter Hamiltonian
that is the most general one-, two-, three- and four-body Hamiltonian. The
package, includes the optimization program tri_min_T, and other
utilities to work with the two dimensional limit of the vibron model.
Copyright (2007-) Francisco Perez-Bernal
All Rights Reserved
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
The full text of the GPL is given in
/usr/share/common-licenses/GPL or in the FSF website GPL license definition.
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triat_U3_min User's Guide
The program files can be found as a tgz file
(triat_U3_min_2.X.tgz, where X stands for
the version number). The first step is to unpack the file:
$ tar xzf triat_U3_min_2.1.tgz
$ ls
triat_U3_min_2.1 triat_U3_min_2.1.tgz
$ cd triat_U3_min_2.1/
triat_U3_min_2.1$ ls
bin/ doc/ examples/ NEWS README src/
The directory structure is the following
bin: Executable files.
src: Fortran source files and compilation
Makefile.
doc: Program documentation (this file) in several formats.
examples: Two different examples of application of the program.
XCNO: Application to the large amplitude bending mode of fulminic acid.
HCP_A: Application to the bending mode of the A excited electronic state of methinophosphide.
The present section details the programs compilation procedure. There is also
a version of the program compiled statically in the bin directory
(tri_min_Tstat). If you run into trouble during any program
compilation you can move forward to Getting Started,
Chapter 3 using the provided static version of the programs.
The program compilation in Debian systems should be quite smooth
provided that the libraries BLAS, LAPACK and
PACKLIB are installed.
The first two are FORTRAN libraries for numerical linear algebra
and can be found in most Linux Distributions. In the Debian
(Lenny) distribution they are associated with packages
libblas-dev and liblapack-dev or other
(atlas library). More information about BLAS and
LAPACK can be found in the Netlib website.
The third library (only needed for the minimization program) is part of the
CERN scientific routines, providing the Minuit minimization tool.
This library in Debian can be installed with the packages
libpacklib1-dev and libkernlib1-dev, though it is
safer to install the cernlib-base-dev package.
Once the libraries are installed the compilation is quite direct.
triat_U3_min_2.1$ cd src
triat_U3_min_2.1/src$ ls
assign_gen.f enrgy_gen_U3.o minuit_u3.f so3casimirW2WB2.f
chisqre_u3_min_gen.f fcn_sub_gen.f readenerg_gfort.f so3casimirW4.f
cpexp.f hbldu3_gen.f scaleh_gen.f
disdata.f Makefile selectvl.f
enrgy_gen_U3.f maxc.f so3casimirW2.f
c
As can be seen in the Makefile, the executable files
tri_min_T and en_U3_gen_T are located under the
triat_U3_min_2.1/bin directory.
List of executable files:
tri_min_T: Optimization code. Look for the best fit to a ser of
experimental data.
en_U3_gen_T: Compute Hamiltonian eigenvalues given a set of
parameters.
There is also a commented section in the Makefile (named
triat_min_Tstat and energenh_Tstat) used to compile
the static version of the programs. In case you want compile the program
statically, uncomment these lines and type make triat_min_Tstat
energenh_Tstat. Please, notice that in this case it is convenient to
make a backup of the provided statically linked programs
(tri_min_Tstat and en_U3_gen_Tstat) because you will
most likely delete them.
If the programs works correctly you can also, running as root user,
install them, by default under the directory /usr/local/bin. The
Perl launch script of the minimization program will be also installed in this
directory. It is convenient to add to the default $PATH variable
the /usr/local/bin in case it is not yet in it. This greatly
facilitates the minimization program's execution instructions explained in Program Execution, Section 3.1.1.4 and Examples, Section 3.1.2, because in this case the
relative paths are not necessary. In order to install it you should do it as
superuser or using sudo
triat_U3_min_2.1/src$ sudo make install
[sudo] password for curro:
triat_U3_min_2.1/src$ ls /usr/local/bin/
minuit_U3_genH* tri_min_T* tri_min_Tstat*
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triat_U3_min User's Guide
tri_min_T
Under the directory triat_U3_min_2.1/examples two examples of use
of this program can be found, one for a linear molecule (fulminic acid fifth
normal vibrational degree of freedom) and one for a bent molecule (magnesium
hydroxide). We explain in detail the first case and chiefly highlight the
differences that arise in the second case.
We proceed now to explain the different input files and the way the provided
programs are executed. There are three necessary input files. A file with the
experimental energy files to be fit, a second file with general information for
the program and a third file with the Hamiltonian parameter information
necessary to accomplish the Minuit minimization.
The experimental energies have to be included in a file. This file starts with a first line which is an integer equals to the number of available experimental levels. Thereafter the experimental information is given, using the following format:
energy error n_quanta l_value
The fields n_quanta and l_value indicate the number of quanta of vibration and the vibrational angular momentum that characterize the state. The number of quanta could correspond to the labeling for linear or bent molecules, as indicated later in the input file.
If the experimental error is fixed to zero, then the level in question is included in the display and compared to the calculated values but the result of this comparison is not included in the calculation of the chi-square and standard deviation, thus making no effect in the fitting procedure.
The general information not referring to Hamiltonian parameters is given in an
input file with a NAMELIST structure. It provides the information
needed to run the program apart from the information directly given to
Minuit for the optimization.
We proceed to check the meaning of the variables are defined in this general input file. A template of it is as follows:
#
## GENERAL INPUT
#
&INP0 BENT=.F., DTFL='expdata.dat' /
&INP1 N2=140, LMAX=5, VMAX=5, EMINL=.F. /
#
&INP2 IPRINT=0 /
Variables defined:
BENT: logical type. If .T.(.F.) the molecule is bent(linear) and experimental data are given accordingly.
DTFL: character type. Name of the file with experimental data.
N2: integer type. N value for the totally symmetric U(3) representation. As version 2.1 the maximum possible N value is 4000.
LMAX: integer type. Maximum value of the vibrational angular momentum (SO(2) quantum number) considered.
VMAX: integer type. Highest experimental overtone included in the fit.
EMINL: logical type. If this variable is .T. the spectrum energies are referred to the first eigenvalue for each vibrational angular momentum block. The default behavior is for EMINL=.F., that implies that all the eigenvalues are referred to the energy of the ground state for vibrational angular momentum zero.
IPRINT: integer type. Program output verbosity. Mainly for debugging purposes. Possible values in the interval 0-5.
The information provided to Minuit for the algebraic spectroscopic
parameter optimization is given in a file. The structure of this file is a
three column list including the parameter labels, its initial values and
initial minimization steps for the fourteen possible Hamiltonian parameters.
This is followed by a statement using the Minuit command
fix to indicate what parameter should be kept constant at the
initial value. The file ends with the Minuit commands for the
optimization. More information can be found in the Fortran Minuit
Manual.
SET TITLE
'MINUIT MINIMIZATION. BENDING DYNAMICS'
PARAMETERS
1 'P11 ' 6.129D+02 0.1D-02
2 'P21 ' 9.9D+00 0.1D-02
3 'P22 ' 0.30D+00 0.1D-02
4 'P23 ' -1.03D+00 0.1D-02
5 'P31 ' 0.0D+00 0.0D+00
6 'P32 ' 0.0D+00 0.0D+00
7 'P33 ' 0.0D+00 0.0D+00
8 'P41 ' 0.0D+00 0.0D+00
9 'P42 ' 0.0D+00 0.0D+00
10 'P43 ' 0.0D+00 0.0D+00
11 'P44 ' 0.0D+00 0.0D+00
12 'P45 ' 0.0D+00 0.0D+00
13 'P46 ' 0.0D+00 0.0D+00
14 'P47 ' 0.0D+00 0.0D+00
fix 5 7 8 9 10 11 12 13 14
#set err 1.0D-05
minimize 3000
call 3
exit
The parameters have labels Pnm, where n =
1,2,3,4 indicates that the operator is n-th body, and m
is an index to distinguish between the different operators of the same order.
From the Hamiltonian building subroutine hbldu3_gen.f:
H = P11 n +
P21 n^2 + P22 l^2 + P23 W^2 +
P31 n^3 + P32 n·l^2 + P33 (n·W^2 + W^2·n) +
P41 n^4 + P42 n^2·l^2 + P43 l^4 + P44 l^2·W^2 +
P45 (n^2·W^2 + W^2·n^2) + P46 W^4 +
P47 (W^2·Wbar^2 + Wbar^2·W^2)/2
where n is the U(2) number operator, l is the vibrational angular momentum, W^2 is the second order Casimir operator associated so SO(3), and Wbar^2 is the Casimir operator of the SObar(3) subalgebra.
The Perl script minuit_U3_genH, under the directory
triat_U3_min_2.1/bin, is provided as a convenient interface to
launch the Fortran program. It creates a temporary directory
where the program runs and, in this way, several instances of the program can
be executed simultaneously.
If the script is executed with no argument it displays a brief help message.
triat_U3_min_2.1/examples/XCNO$ ../../bin/minuit_U3_genH
Usage: ../../bin/minuit_U3_genH [-vts] [-e prgfile] \
minpar_file input_file output_file
Options:
-v: verbose output
-t: do not remove temporary directory
-s: static program version
-e: explicit minimization program given
The important options are -e and -t. The first one
implies that the user will provide the name (and path) of the executable
program file to be launched, while the second option indicates -mainly for
debugging purposes- that the temporary directory tmpdir_XXXX is
not going to be removed once the program execution finishes. The
option,-s, implies the use of the statically linked program
tri_min_Tstat. Finally, the option -v forces a
verbose output.
The script is invoked with three arguments. The first, minpar_file
is the file with the parameter input for Minuit (see Minuit Parameter Input File, Section 3.1.1.3). The
second argument, input_file, is the general input (see General Input File, Section 3.1.1.2). The last
argument is output_file, the name of the file with the program
output. See Examples, Section 3.1.2 to check the
application of the program to two cases, one corresponding to a linear molecule
and the other to a bent molecule.
The files necessary to run this example are located under the directory
examples/XCNO
triat_U3_min_2.1$ cd examples/XCNO/
triat_U3_min_2.1/examples/XCNO$ ls
exp_FulminicD_Feb03.dat minuit_genpar_FulminicD
exp_FulminicH_Feb03.dat minuit_genpar_FulminicH
input_U3_minuit_FulminicD output_FulminicD.orig
input_U3_minuit_FulminicH output_FulminicH.orig
The files exp_FulminicH_Feb03.dat and
exp_FulminicD_Feb03.dat contain the available experimental
information for the large amplitude bending vibration of fulminic acid and its
deuterated isotopologue, and they conform to the standard described in Experimental Energy File, Section 3.1.1.1. The
general input file (see General Input File, Section
3.1.1.2) in this case is called input_U3_minuit_FulminicH (and
input_U3_minuit_FulminicD in the deuterated molecule case).
The information for the algebraic spectroscopic parameter optimization is provided in files minuit_par_FulminicH and minuit_par_FulminicD for HCNO and DCNO, respectively.
The program is executed invoking the Perl script with the already
mentioned three arguments.
The verbose execution of the program for the fulminic acid case for both species is launched with the following commands:
triat_U3_min_2.1/examples/XCNO$ ../../bin/minuit_U3_genH -v \
> -e ~/triat_U3_min_2.1/bin/tri_min_T \
> minuit_genpar_FulminicD input_U3_minuit_FulminicD output_FulminicD
Minuit CHISQRE minimization. U(3) General Hamiltonian.
Making temporary directory ... Done.
Experimental energy file name is: exp_FulminicD_Feb03.dat
Copying files to temporary directory ... Done.
Running optimization program ... Done.
Copying output file from temporary directory ... Done.
Removing temporary directory ... Done.
triat_U3_min_2.1/examples/XCNO$
triat_U3_min_2.1/examples/XCNO$ ../../bin/minuit_U3_genH -vs
minuit_genpar_FulminicD \
> input_U3_minuit_FulminicH output_FulminicH
Minuit CHISQRE minimization. U(3) General Hamiltonian.
Making temporary directory ... Done.
Experimental energy file name is: exp_FulminicH_Feb03.dat
Copying files to temporary directory ... Done.
Running optimization program ... Done.
Copying output file from temporary directory ... Done.
Removing temporary directory ... Done.
In the HCNO case the static version of the program is employed. The final part
of the output in these two cases, once convergence is reached, is included in
files output_Fulminic_HCNO.orig and
output_Fulminic_DCNO.orig.
Notice that the quality of the fit is given in terms of the standard deviation and not the rms. To compute the rms of the fit it is necessary to multiply the standard deviation by the square root of the total number of experimental data and divide it between the square root of the total number of experimental data minus the number of free parameters.
The files necessary to run this example are located under the directory
HCP_A.
triat_U3_min_2.1$ cd examples/HCP_A/
triat_U3_min_2.1/examples/HCP_A$ ls
exp_HCP_A_bending.dat minuit_genpar_HCP_A
input_U3_minuit_HCP_A output_HCP_A_orig
The program is executed in the same way than in the linear case
triat_U3_min_2.1/examples/HCP_A$ ../../bin/minuit_U3_genH -v
minuit_genpar_HCP_A \
> input_U3_minuit_HCP_A output_HCP_A
Minuit CHISQRE minimization. U(3) General Hamiltonian.
Making temporary directory ... Done.
Experimental energy file name is: exp_HCP_A_bending.dat
Copying files to temporary directory ... Done.
Running optimization program ... Done.
Copying output file from temporary directory ... Done.
Removing temporary directory ... Done.
Last part of the output is saved on file output_HCP_A_orig.
en_U3_gen_T
Under the directory triat_U3_min_2.1/examples/Eigenvalues one
example of use of this program can be found.
The input file for this program is rather simple. An example input file with all parameters equal to zero is provided
20 # N INPUT FILE
0 # l
1 # iopts
0.0d0 # P11
0.0d0 # P21
0.0d0 # P22
-10.0d0 # P23
0.0d0 # P31
0.0d0 # P32
0.0d0 # P33
0.0d0 # P41
0.0d0 # P42
0.0d0 # P43
0.0d0 # P44
0.0d0 # P45
0.001d0 # P46
0.0d0 # P47
The parameter N is the value of the totally symmetric U(3) representation used to model the system. As version 2.1 the maximum possible N value is 6000. The vibrational angular momentum is given by the l value.
The parameter iopts controls the output of the eigenvalues. Possible values are
iopts = 0 the program displays only the ground state energy.
iopts = 1 the program displays all energies.
iopts = 2 the program displays all excitation energies (with g.s. (l=0) energy = 0)
In case of debugging purposes, in the source file enrgy_gen_U3.f
there is a variable fixed at zero, called IPRINT. Nonzero
positive values increase the level of verbosity of the program.
This Fortran program is directly launched, providing the described
input file as the standard input. If we execute the program with the input
file found above the result is
triat_U3_min_2.1/examples/Eigenvalues$ ../../bin/en_U3_gen_T < input_file_doc
0.0000000000000000
720.56399999999985
1377.5839999999994
1967.6999999999998
2487.9359999999997
2935.6999999999998
3308.7840000000001
3605.3640000000000
3824.0000000000000
3963.6360000000000
4023.5999999999999
See Examples, Section 3.2.2 to check the application of the program to an example corresponding to a bent molecule.
The files necessary to run this example are located under the directory
examples/Eigenvalues
triat_U3_min_2.1/examples/Eigenvalues$ ls
input_file input_file_doc input_file_HCP
The obtention of the eigenvalues that correspond to the parameters obtained in the fit to the HCP A state are, for zero vibrational angular momentum
triat_U3_min_2.1/examples/Eigenvalues$ ../../bin/en_U3_gen_T < input_file_HCP
0.0000000000000000
566.85562373229914
1028.5555120308779
1484.2632344381639
2046.9932672140753
2689.7360152596357
3382.0393187789541
4103.8525588498451
4838.4084093582642
5569.7433116564898
6281.1719539978449
6953.5491948507433
7562.3703503418556
8078.6701738697175
8529.0156142688957
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triat_U3_min User's Guide
J. Chem. Phys. 104 (1996) 6956.
Chem. Phys. Lett. 365 (2002) 57-68.
Chem. Phys. Lett. 375 (2003) 309-320.
Phys. Rev. A77 (2008) 032115.
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triat_U3_min User's Guide
francisco.perez@dfaie.uhu.es