OneDMin: A code for calculating Lennard-Jones parameters from detailed intermolecular potentials via one-dimensional minimizations A. W. Jasper and J. A. Miller The most recent version of this code may be downloaded from https://tcg.cse.anl.gov/papr/codes/onedmin.html I. Introduction Lennard-Jones parameters for use in combustion modeling, as transport parameters and in pressure-dependent rate-coefficient calculations as collision rate parameters, are calculated from accurate full-dimensional intermolecular potentials via one-dimensional minimizations averaged over the colliding partners' relative orientations. This method includes the effect of local anisotropy in the interaction potential and was shown to lead to very accurate predictions of Lennard-Jones collision rates as compared with tabulated values and with higher-level classical diffusion coefficients. II. References and acknowledgment The preferred citation for this code and for the one-dimensional minimization method is (1) A. W. Jasper and J. A. Miller, Combust. Flame 161, 101 (2014). This method was validated in Ref. 1 by comparisions with tabulated collision rates. It was further validated by comparisions with exact classical diffusion coefficients. See (2) A. W. Jasper, J. A. Miller, and S. J. Klippenstein, J. Chem. Phys., submitted (2014). By default, the code makes use of the "universal" TB+exp/6 potential for hydrocarbons and atomic and diatomic baths described in (3) A. W. Jasper and J. A. Miller, J. Phys. Chem. A 115, 6438 (2011) and validated in (4) A. W. Jasper, C. M. Oana, and J. A. Miller, Proc. Combust. Inst. 34, online (2014). Development of this software was supported by the AITSTME project as part of the Predictive Theory and Modeling component of the Materials Genome Initiative. III. Theory Note: Equation numbers follow Ref. 1 of Sec. II. For a rigid target species A and a rigid bath gas B, the interaction potential is defined in terms of a relative orientation, W, and center of mass distance, r. In the present approach, W is sampled uniformly and the interaction potential is minimized with respect to r for each sampled orientation (EQ 14). The resulting values of the local one- dimensional minimum energies are averaged to obtain the estimate for the Lennard-Jones well depth epsilon (EQ 15a). Similarly, the inner turning point along each approach (for each value of W) is calculated and averaged to obtain the estimate for the Lennard-Jones distance parameter sigma (EQ 15b). An option for including temperature dependence in the internal structures of the target and bath gas is available (EQ 16). By default, the TB+exp/6 intermolecular potential is used. This potential has parameters for CxHy + He, Ne, Ar, Kr, H2, N2, and O2. The potential routine is external to the main code, and expert users can compile the code with other potential subroutines (e.g., to enable direct dynamics, etc). IV. Compilation and execution 1) Edit src/Makefile to reference available compilers and libraries 2) Type gmake in src/ 3) The executable should appear in exe/ 4) To run the code type onedmin-tbplusexp6all.x.opt < input > output where 'input' is the name of the input file, formatted as described in the next section, and output will contain all the standard output. V. Input files A sample input file is included with this distribution in the /runs directory. The regular input file has the format: RANSEED ! Random number seed MA GEOFILEA ! Geometry information for the target (see below) MB GEOFILEB ! Geometry information for the bath (see below) N ! Number of orientation samples RMIN RMAX ! Minimum and maximum allowable values of the A-B center of mass distance ZERO ! Zero of energy (set to the energy of A+B) in Hartrees For example: 194843 ! Random number seed 1 ch4.eq ! Geometry information for the target (see below) 1 he.eq ! Geometry information for the bath (see below) 1000 ! Number of orientation samples 2. 5. ! Minimum and maximum allowable values of the A-B center of mass distance 0. ! Zero of energy (set to the energy of A+B) in Hartrees If EQ 14 is used, then MA=MB=1 and the files GEOFILEA and GEOFILEB should contain the equilibrium geometries of the target and bath species in Molden format. If EQ 15 is used, then MA>1 and the geometry of the target will be randomly sampled over the MA geometries listed in GEOFILEA along with the randomly sampled orientations; likewise for the bath. 'Molden format' for each file GEOFILEA and GEOFILEB is as follows: Title line #1 Title line #2 NATOMS STEP1 ATOMNAME X Y Z ... NATOMS STEP2 ATOMNAME X Y Z ... etc. where NATOMS is the number of atoms and X, Y, and Z are Cartesian coordinates in Angstroms. The title lines and step numbers are not used by this code. For example, GEOFILEA for CH4 with MA=1 could be: TB+exp/6 equilibrium geometry for CH4 The Cartesian coordinates are Angstroms 5 1 Geometry step number; not used C 0.0000 0.0000 0.0000 H 0.6276 0.6276 0.6276 H 0.6276 -0.6276 -0.6276 H -0.6276 0.6276 -0.6276 H -0.6276 -0.6276 0.6276 GEOFILEB for He with (necessarily) MA=1 is simply: He Empty 2nd title line 1 1 Geometry number; not used He 0.0000 0.0000 0.0000 VI. Output A sample output file is included with this distribution in the /runs directory. The standard output is straightforward. One can turn on additional output by setting the hardcoded flag ldebug to .true. in onedmin.F.