An accurate analytic He-H2 potential energy surface from a greatly expanded set of ab initio energies

Arnold I. Boothroyd (CITA), Peter G. Martin (CITA), and Michael R. Peterson (Dept. of Computing and Networking, U. of Toronto)

Journal of Chemical Physics, 119, 3187-3207   (2003)

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Abstract: The interaction potential energy surface (PES) of He-H2 is of great importance for quantum chemistry, as the simplest test case for interactions between a molecule and a closed-shell atom. It is also required for a detailed understanding of certain astrophysical processes, namely collisional excitation and dissociation of H2 in molecular clouds, at densities too low to be accessible experimentally. A new set of 23703 ab initio energies was computed, for He-H2 geometries where the interaction energy was expected to be non-negligible. These have an estimated rms ``random'' error of about 0.2 millihartree and a systematic error of about 0.6 millihartree (0.4 kcal/mol). A new analytic He-H2 PES, with 112 parameters, was fitted to 20203 of these new ab initio energies (and to an additional 4862 points generated at large separations). This yielded an improvement by better than an order of magnitude in the fit to the interaction region, relative to the best previous surfaces (which were accurate only for near-equilibrium H2 molecule sizes). This new PES has an rms error of 0.95 millihartree (0.60 kcal/mole) relative to the the 14585 ab initio energies that lie below twice the H2 dissociation energy, and 2.97 millihartree (1.87 kcal/mole) relative to the full set of 20203 ab initio energies (the fitting procedure used a reduced weight for high energies, yielding a weighted rms error of 1.42 millihartree, i.e., 0.89 kcal/mole). These rms errors are comparable to the estimated error in the ab initio energies themselves; the conical intersection between the ground state and the first excited state is the largest source of error in the PES.

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This paper describes the BMP He-H2 surface, and the He-H2 ab initio data on which the surface is based. [Note that there is an error in Equation (9) of the published version of this paper: a factor of 1/Rnu should be removed from this equation. This error has been fixed in the versions available from this website.] The paper is available as:

• a PDF file (1.6 Mb) -- 44 pages (including figures)
• a gzip-compressed PostScript file (0.52 Mb, expands to 2.9 Mb) -- 44 pages (including figures)
• Also available from the LANL preprint archives, as astro-ph/0305386 (preprint CITA-2003-19)

See also the plain text file README.TXT (3.4 kb) for a description of available BMP He-H2 Fortran routines and data. These can be downloaded using the links below, and are also available as EPAPS entry E-JCPSA6-119-309330, via this http URL or this ftp URL

BMP He-H2 Fortran program:

• The Fortran routines heh2bmp.f (0.11 Mb) for the BMP analytic He-H2 surface (description and instructions are in the comments at the beginning of this file)
• and the Fortran test program heh2bmp_test.f (0.18 Mb) to check that the BMP He-H2 surface is being evaluated correctly on your computer
• (optional): a plain text file heh2bmp_test.out (1.5 kb) containing an example of typical output produced by the above test program.
• Alternatively: the gzip-compressed tar archive heh2prog.tar.gz (66 kb, expands to 0.31 Mb) contains all three of the above files.

He-H2 ab initio data:

• The plain text file heh2ptsREADME.txt (17 kb) contains a description of the files in the two tar archives below:
• All ground state and generated energies: the gzip-compressed tar archive ciheh2usen.tar.gz (1.0 Mb, expands to 4.0 Mb) contains 13 files of He-H2 ground state energies (plus the above file heh2ptsREADME.txt): all He-H2 ground state energies used in the BMP He-H2 surface fit.
• Our ab initio ground state plus excited state energies: the gzip-compressed tar archive ciheh2ean.tar.gz (7.9 Mb, expands to 38.2 Mb) contains 12 files of complete He-H2 energy sets (plus the above file heh2ptsREADME.txt): all our own He-H2 ab initio energies (including ground state and lowest 4 excited states).

Legendre coefficients for analytic surfaces:

For comparison purposes, plain text files containing tables of Legendre coefficients for H2 + He can be downloaded for the BMP analytic H3 surface, our modified Muchnick/Russek (mMR) surface, the Muchnick/Russek (M+R) surface, and the Schaefer/Kohler (S+K) surface. For each surface, separate files are given with V0 (the spherical average), V2, and V4; in each file, five separate hydrogen molecule sizes are included (0.9, 1.28, 1.449, 1.618, and 2.0 bohrs), with H - H2 separations R in the range 1.6 bohrs < R < 20 bohrs. (These four surfaces are discussed in our above paper.)

Surface	V0	V2	V4
BMP	v0_heh2_BMP.txt	v2_heh2_BMP.txt	v4_heh2_BMP.txt
mMR	v0_heh2_mMR.txt	v2_heh2_mMR.txt	v4_heh2_mMR.txt
M+R	v0_heh2_M+R.txt	v2_heh2_M+R.txt	v4_heh2_M+R.txt
S+K	v0_heh2_S+K.txt	v2_heh2_S+K.txt	v4_heh2_S+K.txt

Those interested in Legendre coefficients for H2-molecule sizes other than the five listed above can download:

• vlam_heh2.f (10 kb), the He-H2 Legendre coefficient integration program;
• vheh2SK.f (25 kb), the Schaefer/Kohler He-H2 surface (which is also required);
• debasix.f (27 kb), containing the Schwenke H-H potential (also required);
• note that the BMP He-H2 surface (download above) is of course needed as well.