DJ |
Diatomic approximation to weakly bound dimers: Rcm, kσ, ωσ, ε from rotational constants and DJ
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The
program implements the useful formulae used to derive several key
properties of weakly bound dimers by means of the diatomic
approximation based on the Lennard-Jones potential. The key relationships connect the centrifugal
distortion constant DJ with the intermolecular stretching force constant kσ and those exist in several subvariants developed in order to account for various shapes of the monomers. Associated expressions allow evaluation of the centre of mass separation Rcm, of the intermolecular stretching frequency ωσ, of correction of the ground state rotational constant of the dimer to equilibrium, and of the Lennard-Jones well depth ε.
The use of these formulae dates back to
1970's and papers from the Klemperer group, but I have not been able to
locate a paper summarising, let alone benchmarking, all of the
possibilities. For this reason DJ calculates the results in several variants and
identifies the equation and the paper explicitly after the result.
It is up to the user to select the most suitable result.
DJ
requires specification of the masses and of the rotational constants of
the monomers and of the dimer. If large amplitude averaging
angles for monomers in the dimer are available then those can also be
specified and will be used.
References:
- S.E.Novick, P.Davies, S.J.Harris,W.Klemperer, Determination of the structure of ArHCl, J.Chem.Phys. 59 (1973) 2273-2279: early application of the diatomic model and of the large amplitude averaging correction for HCl.
- T.J.Balle, E.J.Campbell, M.R.Keenan, W.H.Flygare, A new method for observing the rotational spectra of weak molecular complexes, J.Chem.Phys. 72 (1980) 922-932: comprehensive
exposition of the diatomic model and evaluation of the diatomic
stretching frequency and of the Lennard-Jones dimerisation energy.
- W.G.Read, E.J.Campbell, G.Henderson, The rotational spectrum and molecular structure of the benzene-hydrogen chloride complex, J.Chem.Phys. 78 (1983) 3501-3508: the commonly used modification of the DJ-kσ relationship accounting for asymmetry in the larger molecule in the dimer.
- D.J.Millen, Determination of stretching force constants of weakly bound dimers from centrifugal distortion constants", Canad.J.Chem. 7 (1985) 1477-1479: several variants of the DJ-kσ relationship accounting for various departures of dimer symmetry from a simple diatomic.
- S.G.Kukolich, E.J.Campbell, Microwave measurements
of bromine quadrupole coupling constants and the molecular structure of
XeHBr", Chem.Phys.Lett. 94 (1983) 73-76: more
explicit expressions than in ref.[2] for correcting the ground state
rotational constant of the dimer to an equilibrium value and for the
Lennard-Jones well depth ε.
- E.J.Goodwin, A.C.Legon, The rotational spectrum of
the weakly bound molecular complex OC...HCN investigated by
pulsed-nozzle, Fourier-transform microwave spectroscopy, Chem.Phys. 87 (1984) 81-92: Example of the use of the large amplitude averaging correction for both complexed molecules.
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DJ.FOR |
The
listing. |
DJ.EXE |
Win32 executable. |
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Examples |
DJ.INP |
The input
data file. Each dimer is defined by a single data line.
There can be as many such lines as necessary, which will be processed
until a negative B_ab value is encountered.
Input of the numerical data is column sensitive so please fit numbers
within the columns defined by the guiding line in the header (and do use
non-proportional fonts in your text editor).
The data lines can be interspersed with an unlimited number of comment
lines beginning with the ! character in the first column. These
lines are not echoed to the output.
Some hints:
- For a dimer to an atom use a very large value of B (such as 1.E+20) for the atom.
- For a (prolate) molecule monomer use (B+C)/2 for B.
- All the distances from DJ
are centre of mass separations while the distances cited in the
original papers may be different (such as heavy atom distances) .
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DJ.OUT |
The output file resulting from the input file above. |
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RGDMIN |
Prediction of geometry
of Rg...molecule dimers with a simple distributed model for dispersive
interaction
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The
program minimises interaction energy between a rare-gas atom and a
molecule, which is assumed to consist of dispersive attraction
counterbalanced by hard sphere repulsion. The anisotropy of the
dispersive interaction is modeled by replacing atomic polarisabilities
by cubes of their covalent radii.
References:
- Z.Kisiel, J.Phys.Chem. 95,
7605-7612 (1991) - the model
- Z.Kisiel, P.W.Fowler, A.C.Legon, J.Chem.Phys.
95, 2283-2291 (1991) - use of the model to
rationalise geometries of Ar...CH2CHF, Ar...CH2CF2,
Ar...CHFCF2
Principal features:
- automatic assignment of model parameters,
which can be overridden
- fixed geometry calculation
- full and limited minimisation (eg. for
potential characterisation)
- Rg-atom translation vector can be either
Cartesian or polar
- input of translation vector from keyboard or
file
- output to screen and two types of files
RGDMIN
runs interactively and can use up to four different files:
- Main input file with containing molecular
data, specified at run-time by the user
- Optional file containing initial starting
positions of Rare gas atom B, user named
- Main output file containing results of
minimisations, user named
- Ancillary output file containing details of
individual iterations, this has a fixed name: MONITOR
RGDMIN is
a much simplified derivative version of MIN16.
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RGDMIN.FOR |
The
listing. |
RGDMIN.EXE |
Win32 executable. |
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Examples |
OFTKR.RGD |
Data file
for o-F-toluene...Kr |
OFTKR.RES |
Results
file containing the principal geometries identified using starting
positions in STARTG.RGD. |
STARTRG.CFG |
An array
of starting coordinates for minimisation of dimer geometry. The idea is
to provide either a hemisphere or a sphere of starting points so that
the most important local minima will be located. |
MONITOR |
The MONITOR file
summarising the geometries for the complex above located with STARTRG.CFG.
Note that, in general, quite a few
local minima will be found. The majority are physically sensible, but
some may be an artifact of the hard sphere repulsion used in the model
- see Fig.8 of the paper on the model.
In the present case RUN.1 converges
to the global minimum, RUN.4 is probably a spurious minimum very close
to the global one, RUN.23 is a competing local minimum, RUN.29 is an
insignificant local minimum.
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MIN16 |
Geometries of hydrogen
bonded dimers from the electrostatic model of Buckingham and Fowler
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This
program is descended directly from Patrick Fowler's program V used in
the development of the electrostatic model.
The
B&F model is based on the idea that the dominant contribution to
interaction energy comes from the electrostatic term. This can be
rather satisfactorily modeled by using the distributed multipole
analysis (DMA) of electron charge distribution, and the resulting
attractive electrostatic term is counterbalanced by a hard van der
Waals sphere repulsive term. The program searches for minima in
intermolecular interaction energy between molecules A and B by
reorienting molecule B around molecule A.
Note
that a rather more developed program for such calculations, ORIENT, is available from Anthony Stone in Cambridge.
References:
- Buckingham and Fowler, J.Chem.Phys.
79, 6426 (1983) - electrostatic model
- Buckingham and Fowler, Can.J.Chem.
63, 2018 (1985) - electrostatic model
- Price and Stone, J.Chem.Phys. 86,
2859 (1987) - repulsive wall as used in MIN16
- Stone, Chem.Phys.Lett. 83,
233 (1981) - DMA
- Kisiel, Fowler, Legon, J. Chem. Phys.
93, 3054 (1990); 93, 6249
(1990); 101, 4635 (1994) - some of the first
applications of this program
- A.D.Buckingham - in Intermolecular
Interactions - From Diatomics to Biopolymers: Pullman, B., Ed.;
Wiley: New York, 1978; Chapter 1 - invaluable tutorial on concepts and
procedures used in MIN16
Key
features of MIN16:
- calculation of electrostatic interaction
energy (Ees)int up to quadrupole
- calc of (Ees)int
with all terms up to t4 = tabgd
(ie all quadrupole terms and charge.octopole + dipole.octopole +
charge-hexadecapole)
- calc of (Ees)int
with all terms up to octopole (t6)
- calc of (Ees)int
limited by t6 and hexadecapole
- calc of (Ees)int
limited by t7 and hexadecapole
- calc of (Ees)int
with all terms up to hexadecapole (t8)
- full minimisation (6 parameters = 3 in
translation vector, and 3 rotation angles of molecule B relative to A)
- limited minimisation - only one of the three
translation vector parameters (R) is minimised
- fixed geometry calculation
- translation vector input in either Cartesian
or polar form
- input of translation vector from keyboard or
file
- output to screen and two types of files
- recovery of molecular multipoles from
distributed multipoles
- inspection of selected structural parameters
MIN16 is
accompanied by several programs for extracting DMA's from output of
various ab initio packages and for managing DMA arrays.
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MIN16.FOR |
The
listing - this is a straightforward numbercrunching program and has
been compiled on several hardware/software architectures including
Pentium/SG/DOS/UNIX. The use of the -static option for the f77 compiler family
is mandatory. |
MIN16.EXE |
Executable for Win98/Win2K/XP. |
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Examples |
MECPHF.HEX |
Sample data file, for
the methylenecyclopropane...HF hydrogen bonded dimer. This was used to
produce the results reported in Chem.Phys.Lett. 232,
187 (1995). |
MECPHF.RES |
Abbreviated results
file for the above, with runs identifying the two geometries reported
in the paper.
Each section containing the
Cartesians for the minimised geometry can be cut out and viewed
directly with PMIFST.
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MECPHF.MON |
The monitor file
showing abbreviated results of minimisations carried out from starting
points in START.CFG. Note how these results split between the two geometries. |
START.CFG |
File containing an
array of starting configurations for the minimisation. The idea is to
provide either a hemisphere or a sphere of starting points so that the
most important local minima will be located.
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Companion programs |
EXTRACT.FOR |
Extraction of DMA
from output of CADMAC, SYSMO (and possibly GAMESS UK) and conversion
into the form used by MIN16. Not used for some time and might need some modification. |
GAMDMA.FOR |
Extraction of DMA
from GAMESS output and conversion into the form for MIN16.
This has almost exclusively been used with PC GAMESS - note that GAMESS
only produces DMA's up to octopole and the hexadecapoles are set to
zero. |
DMAROT.FOR |
Program for
transformations (rotation, translation, shift of expansion origin) on a
DMA array. |
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