Diatomic approximation to weakly bound dimers: Rcm, kσ, ωσ, ε from rotational constants and DJ 

        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.


  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.

DJ.FOR The listing.
DJ.EXE Win32 executable.
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) .
DJ.OUT The output file resulting from the input file above.

Back to the table of programs





Prediction of geometry of Rg...molecule dimers with a simple distributed model for dispersive interaction

        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.


  • 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.


RGDMIN.FOR The listing.
RGDMIN.EXE Win32 executable.
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.


Back to the table of programs





Geometries of hydrogen bonded dimers from the electrostatic model of Buckingham and Fowler

        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.


  • 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.


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.
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.

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.
  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.

Back to the table of programs