========================================================================= He-H2: Description of the files containing the He-H2 energy values of BMP ========================================================================= The files described below contain the He-H2 energies used and described in: A. I. Boothroyd, P. G. Martin, and M. R. Peterson (2003), "An accurate analytic He-H2 potential energy surface from a greatly expanded set of ab initio energies", J. Chem. Phys., in press. Archive Name Size Description ----------------- -------- ------------------------------------------------- ciheh2usen.tar.gz (1.0 Mb): gzip-compressed tar-file archive containing the files 1 through 14 below (total size 4.0 Mb): all He-H2 ground state energies used in the BMP He-H2 surface fit. ciheh2ean.tar.gz (7.9 Mb): gzip-compressed tar-file archive containing the files 14 through 26 below (total size 38.2 Mb): all our own He-H2 ab initio energies (including ground state and lowest 4 excited states). To extract files requires the gzip utility to decompress the archive, and the tar utility to extract the files. For example, on a Unix or Linux system, to extract all the files from an archive called ARCHIVENAME.tar.gz and delete it: gunzip -v ARCHIVENAME.tar.gz tar xvf ARCHIVENAME.tar rm ARCHIVENAME.tar Contents of the archives: ------------------------- Files 1-12 contain all the energies fitted by the BMP He-H2 surface; file 13 contains our unfitted ("interstitial test") ab initio energies. Files 1, 2, and 13 contain our best He-H2 ab initio ground state energies; corresponding files 15, 16, and 26 contain all our computed He-H2 ab initio energies, in all cases including the lowest 5 roots (i.e., the ground state plus 4 excited states --- note that the order of the roots is not well defined in the case of closely-spaced energies, so in some cases excited states lying just below the reported 5th root may have been missed); these files also contain cases with different CI reference sets and different SCF-types. Files 3-12 contain generated energies, used to constrain the fitted surface in regions where we did not compute ab initio energies. Files 17-20 contain test cases with other bases sets, not used in the fitting. Files 21-25 contain He-H (two-atom) energies with various basis sets; energies from file 21 were used to get many of the energies in files 3 and 4. ALL OF THESE ARE PLAIN TEXT ASCII FILES: File Name Size(bytes) Description ------------------- ----------- -------------------------------------------- 1. ciheh2newpts.usen 2225712: 16703 ab initio energies of main-BMP-grid. 2. ciheh2newrand.usen 469708: 3500 ab initio energies of random-BMP-grid. 3. ciheh2fromheh1.usen 255184: 1887 "H-He" points generated from BMP He-H ab initio energies (for R{He-H} < 4 bohrs) or from Gengenbach He-H (for R > 4 bohrs) by adding a distant H atom. 4. ciheh2nearheh1.usen 114701: 830 "H-He + H" points generated from He-H. 5. ciheh2abSenff.usen 7402: 24 Senff & Burton ab initio energies (given zero weight in the fit, i.e., not fitted). 6. ciheh2abMeyer.usen 14579: 78 Meyer, Hariharan, & Kutzelnigg ab initio energies (given zero weight in the fit). 7. ciheh2abMuRu.usen 24953: 156 Muchnick & Russek composite ab initio energies (given zero weight in the fit). 8. ciheh2abTao.usen 13389: 69 F.-M.Tao [6s4p2d]-{3s3p2d} MP4 ab initio. 9. ciheh2modMuRu.usen 214349: 1580 van der Waals geometries generated from Muchnick & Russek surface (given zero weight in the fit, i.e., not fitted). 10. ciheh2schaef.usen 120708: 876 van der Waals geometries generated from Schaefer & Kohler surface (only 499 of these had non-zero weight in the fit). 11. ciheh2modTao.usen 53952: 374 van der Waals geometries generated from F.-M.Tao ab initio energies. 12. ciheh2mtaoMuRu.usen 214350: 1580 van der Waals geometries generated from modified Muchnick & Russek surface fitted to Tao ab initio energies (only 1203 of these had non-zero weight in the fit). 13. ciheh2tstrand.usen 469710: 3500 UNFITTED ab initio energies of BMP (random, same probability distribution as file 2): NOT used in fit, only to test for "interstitial" wiggles in BMP surface 14. heh2ptsREADME.txt 17781: This README file describing He-H2 points. 15. ciheh2newpts.ean 27669277: 16703 main-BMP-grid points with both ground state and several excited state ab initio energies (incuding different SCF-types and/or CI thresholds and reference sets). 16. ciheh2newrand.ean 5900763: 3500 random-BMP-grid points likewise. 17. ciheh2spdsp2d.ean 15649: 7 points with different basis set. 18. ciheh2spdspd.ean 96779: 60 points with different basis set. 19. ciheh2spsp.ean 97577: 60 points with different basis set. 20. ciheh2spsp2d.ean 15649: 7 points with different basis set. 21. ciheh1allpts.ean 57409: 40 ab initio He-H energies of BMP (incuding different CI thresholds). 22. ciheh1spdsp2d.ean 57409: 40 He-H points with different basis set. 23. ciheh1spdspd.ean 57409: 40 He-H points with different basis set. 24. ciheh1spsp.ean 57409: 40 He-H points with different basis set. 25. ciheh1spsp2d.ean 57409: 40 He-H points with different basis set. 26. ciheh2tstrand.ean 5908745: 3500 ab initio UNFITTED-random-BMP-grid. Description of the format of the files: --------------------------------------- Each file has a number of header lines giving a brief description of the contents, followed by the data; except for some header lines, the line length is 132 characters. The first 72 characters of the last two header lines and of the first four data lines in file 1 (ciheh2newpts.usen) are: Nabs ijk lmn A/2 Y3 Z3 X4 Y4 Z4 S ----- -=-==-= -------- -------- -------- -------- --------- --------- - 5833 301H2He 0.762500 0.000000 1.762500 E 5834 301H2He 0.762500 0.130526 1.753945 E 5835 311H2He 0.762500 0.258819 1.728426 E 5836 311H2He 0.762500 0.382683 1.686380 E and characters 73 through 132 of these six lines are: f(N) sumC*C Eex dEl34 dE(T) DTS |Ddc| DbasL Efinal --- ------- -------- ----- ----- ----- ----- ----- -------- .52 .977097 .181198 111 650 -11 1929 2581 .177579 .52 .977136 .182028 44 1374 -22 1926 2581 .178400 .52 .977101 .184592 13 1664 -13 1931 2581 .180969 .52 .977044 .188967 -6 1706 -11 1938 2582 .185342 NOTE THAT THE LAST HEADER LINE MAY BE FOUND BY checking the first 6 characters in each line; it is the only line whose first 6 characters are ' -----' (the number of lines in this header may differ from file to file). The data lines (following until the end of the file) contain the values: Nabs, ijk, lmn, A/2, Y3, Z3, X4, Y4, Z4, S, f(N), sumC*C, Eex, dEl34, dE(T), DTS, |Ddc|, DbasL, Efinal in the FORMAT (I6,1X,A3,A4,4F9.6,2F10.6,1X,A1,F4.2,F8.6,F9.6,5I6,F9.6) where the geometry (A/2, Y3, Z3, X4, Y4, Z4) and the final energy (Efinal) are the most important quantities; see the following description of the data lines: Nabs (I6) is 5-digit integer, a unique identifier for each geometry; note that the same geometry may appear in several different files. ijk,lmn (1X,A3,A4) are (non-unique) geometry indices, and can be ignored; ijk is a 3-digit positive integer, and lmn is "H2He" or "H1He". A/2 (F9.6) gives the position (in bohrs) of the two H-atoms (in Cartesian coordinates): x1 = y1 = 0 , z1 = -A/2 , x2 = y2 = 0 , z2 = A/2 ; note that A/2 is half the interatomic distance between the two hydrogen atoms. Y3,Z3 (2F9.6) give the position (in bohrs) of the He-atom: x3 = 0 , y3 = Y3 , z3 = Z3 ; note that r23 is never longer than r13, nor shorter than r12. X4,Y4,Z4 (F9.6,2F10.6) are left blank, since there are only three atoms. *****For "H1He" (i.e., He-H), A/2 is half the distance between the H and He atoms, and Y3,Z3 are left blank, as there are only two atoms. S (1X,A1) is a single-character code identifying the type of energy (see full description below of its possible meanings). f(N) (F4.2) is the multiplier lambdaDC:HeH2 used to obtain the correction to full CI from the Davidson correction (see Efinal below). sumC*C (F8.6) is the sum of the reference C-squared values in the multiple-reference CI calculation. Eex (F9.6) is Elambda(T) (in hartrees), the energy extrapolated (using Buenker's method) to zero threshold from the truncated-CI energies E(T) and E(2T) [where only configurations contributing more than the threshold T (or 2T) were included in the truncated-CI calculations]; note that by definition Elambda(T) = Elambda(2T). dEl34 (I6) is Elambda(3T) + Elambda(4T) - 2 * Eex (in microhartrees), a measure of the energy extrapolation error at higher thresholds. dE(T) (I6) is E(T) - Eex = E(T) - Elambda(T) (in microhartrees), the size of the extrapolation to zero threshold from the lowest-threshold truncated-CI energy. DTS (I6) is the sum of any additional corrections (in microhartrees); for the above He-H2 and He-H files, this comprises the tiny "non-linearity" correction to the extrapolation to zero threshold, PLUS (for "...usen" files 1, 2, 13 only) any difference between final weighted average energy actually used and the best of the individual energies (generated energies in files 3 and 4 are an exception: for these, DTS includes the estimated effects of the "added" H-atom). |Ddc| (I6) is the absolute value (in microhartrees) of the "bare" Davidson correction supplied by Buenker's MRD-CI program, namely, abs{ ( 1 - sumC*C ) * [ E(MRDCI) - Ereference ] } . DbasL (I6) is the size (in microhartrees) of the London-type basis-size correction. Efinal (F9.6) (in hartrees) is Eex + DTS - f(N) * |Ddc| / sumC*C - DbasL , the best final corrected ab initio energy value. Note that for any given geometry in files 14 through 24, ALL the coordinates A/2 through Z4 are left blank except for the FIRST energy at that geometry; the LAST energy value for each geometry is usually the best one. Note that in files 1 and 2, the quantities S through |Ddc| refer to the best of the individual energy values from the corresponding files 14 and 15. For very spread-out geometries (10 bohrs or more), there may not be any blanks between the coordinate specifications A/2, Y3, Z3; if the 6th decimal place of the previous coordinate value is zero, this is replaced by a blank to leave a visible space, but a non-zero 6th decimal place is retained. Note that the quantites f(N) through |Ddc| (or their equivalents) were not in general available for the energies supplied by other authors. In these cases, Eex was generally the quoted ***interaction*** energy between He and H2, while dEl34 - f(N) * |Ddc| gave the H2 energy (from Schwenke's formula), and Efinal is the ***total*** energy (directly comparable to our ab initio energies); also the formats of the individual columns differ from the above specifications --- for example, Eex and Efinal may have 7 decimal places, i.e., format (F9.7). Meanings of the single-character type-code S (identifying the type of energy): ------------------------------------------------------------------------------ for He-H2 ab initio energies of other authors: ---------------------------------------------- "t" = H2-He accurate van der Waals ab initio [6s4p2d]-{3s3p2d} MP4 energies of F.-M. Tao (1994), J. Chem. Phys. 100, 4336 "U" = H2-He van der Waals ab initio energies of U. E. Senff & P. G. Burton (1985), J. Chem. Phys. 89, 797 "n" = H2-He van der Waals ab initio energies of W. Meyer, P. C. Hariharan, & W. Kutzelnigg (1980), J. Chem. Phys. 73, 1880 "R" = H2-He van der Waals composite ab initio van der Waals energies of P. Muchnick & A. Russek (1994), J. Chem. Phys. 100, 4336 for energies generated to constrain the HeH2 fit: ------------------------------------------------- "a" = H2-He van der Waals energies based on the Tao (1994) points (using a fitted form as a function of R plus fitted Legendre angular form to get values at R-distances and angles not in the Tao ab initio set) "K" = H2-He van der Waals (for their five rHH values) of J. Schaefer & W. E. Kohler (1985), Physica 129A, 469 "k" = H2-He Schaefer & Kohler van der Waals, for rHH = 1.1 and 1.8 bohrs "F" = H2-He Muchnick & Russek surface van der Waals, for the same geometries as types "K" and "k" above "f" = H2-He Muchnick & Russek surface van der Waals, for extreme values of rHH = 0.6, 0.7, 0.8, 2.4, 3.0, and 4.0 bohrs "m" = H2-He van der Waals with modified Muchnick & Russek surface fitted to Tao(1994) points (same geometries as type "F" above) "e" = H2-He van der Waals with modified Muchnick & Russek surface fitted to Tao(1994) points (same geometries as type "f" above) "g" = H-He Gengenbach van der Waals (with second H at very large distance, i.e., negligible interaction energy with H-He pair) "X" = H-He + H approximate energies (like type "g", but closer in) for our own BMP He-H2 ab initio energies: ----------------------------------------- "C", "L", "d", "c" = single-root MRD-CI energies with extrapolation threshold T = 10.0, 2.0, 0.4, or 0.0 microhartrees, respectively, with the molecular orbitals for the CI calculation obtained from closed-shell SCF (2 closed shells) "o", "p", "P", "O" = molecular orbitals obtained from open-shell SCF (4 open shells); otherwise same as above "b", "B", "h", "H" = molecular orbitals from mixed-shell SCF (1 closed shell, 2 open shells); otherwise same as above "D", "E", "l", "1" = the lowest root (ground state energy) from multiple-root MRD-CI calculation (same T = 10.0, 2.0, 0.4, or 0.0 microhartrees, respectively), with molecular orbitals obtained from closed-shell SCF "I", "J", "[", "2" = the second root (first excited state energy); otherwise same as above "i", "j", "]", "3" = the third root; otherwise same as above "A", "<", "!", "4" = the fourth root; otherwise same as above "#", ">", "|", "5" = the fifth root; otherwise same as above "Q", "q", "0", "6" = the lowest root (ground state energy) from multiple-root MRD-CI calculation (same T = 10.0, 2.0, 0.4, or 0.0 microhartrees, respectively), with molecular orbitals obtained from open-shell SCF "N", "G", "(", "7" = the second root (first excited state energy); otherwise same as above "r", "s", ")", "8" = the third root; otherwise same as above "@", "&", "+", "9" = the fourth root; otherwise same as above "$", "^", "=", "_" = the fifth root; otherwise same as above "M", "T", "x", ";" = the lowest root (ground state energy) from multiple-root MRD-CI calculation (same T = 10.0, 2.0, 0.4, or 0.0 microhartrees, respectively), with molecular orbitals obtained from mixed-shell SCF "V", "u", "{", "`" = the second root (first excited state energy); otherwise same as above "v", "w", "}", "," = the third root; otherwise same as above "y", "*", "/", ":" = the fourth root; otherwise same as above "%", "?", "~", "." = the fifth root; otherwise same as above Note that, when an N-root MRD-CI calculation is performed, the choice of which N roots will have lowest energy is only made using an approximate criterion; thus when levels are closely spaced, the MRD-CI calculation may miss an energy level that is actually slightly lower in energy than the Nth, or even (N-1)th, reported root. Similarly, the single-root MRD-CI calculation very occasionally misses the ground state energy, yielding the first excited state instead; in such a case, a calculation with multiple roots will have yielded the correct ground state energy.