===================================================================== H4: Description of the files containing the H4 energy values of BMKP2 ===================================================================== The files described below contain the H4 energies used and described in: A. I. Boothroyd, P. G. Martin, W. J. Keogh, and M. R. Peterson (2001), "An accurate analytic H4 potential energy surface", J. Chem. Phys., in press. Archive Name Size Description ----------------- -------- ------------------------------------------------- cih4usen.tar.gz (3 Mb): gzip-compressed tar-file archive containing the 11 files 1 through 11 below (total size 8 Mb): all H4 ground state energies used in the BMKP H4 surface fit. cih4ean.tar.gz (17 Mb): gzip-compressed tar-file archive containing the 8 files 11 through 18 below (total size 76 Mb): all our own H4 ab initio energies (including 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 1-10 contain all the energies fitted by the BMKP H4 surface. Files 1-5 contain our best H4 ab initio ground state energies. The corresponding files 12-16 contain all the computed H4 ab initio energies, in all cases including the lowest 5 roots (i.e., 4 excited states as well as the ground state --- 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 6-10 contain generated energies, used to constrain the fitted surface in regions where no ab initio energies were available. Files 17 and 18 contain test cases not used in the fitting (including excited states for file 17). File Name Size(bytes) Description ------------------- ----------- -------------------------------------------- 1. cih4omcalln.usen (814206): 6101 geometries: the old grid of Boothroyd et al. 1991 (though with udated energies) 2. cih4omcnewn.usen (1255631): 9420 geometries: new gridpoints and added conformations to fill gaps in coverage 3. cih4omcaddn.usen (345914): 2580 geometries: more added conformations 4. cih4omch3hn.usen (334447): 2494 geometries: added conformations that begin to resemble H3+H 5. cih4newrand.usen (3671578): 27585 geometries: added random conformations 6. cih4newfarh3.usen (945474): 7088 geometries: H4 conformations generated randomly from our H3 ab initio energies, i.e., with a 4th H atom placed randomly at a large distance from the H3 conformation 7. cih4partriabh3.usen (69673): 503 geometries: H4 conformations generated randomly from the H3 ab initio energies of Partridge et al. 1993 (and Partridge 1994) 8. cih4partrmtth3.usen (131518): 968 geometries: H4 conformations generated randomly from the H3 energies obtained via the MTT fit to the ab initio energies of Partridge et al. 1993 9. cih4schaefnew.min (483037): 3611 geometries: accurate large-seperation H2+H2 energies generated from the modified Schaefer and Kohler surface, to constrain the van der Waals region 10. cih4closlond.min (161283): 1197 geometries: low-accuracy very-short- distance energies obtained from the London equation, to constrain the extrapolation to short distances 11. h4ptsREADME.txt (18243): This README file describing the H4 points. 12. cih4omcalln.ean (8272314): 6101 geometries, 62177 energies 13. cih4omcnewn.ean (13023205): 9420 geometries, 97898 energies 14. cih4omcaddn.ean (3753640): 2580 geometries, 28202 energies 15. cih4omch3hn.ean (2463112): 2494 geometries, 18499 energies 16. cih4newrand.ean (33177362): 27585 geometries, 249433 energies 17. cih4tstadd.ean (16999774): 13356 geometries, 127797 energies: test conformations not used in the fit (mostly used to map out the conical intersection between the ground state and the first excited state); NOT USED IN FIT 18. cih4sp.ean (100313): 519 geometries, 733 energies: (9s3p)/[4s3p] ab initio energies (ground state only) to test the basis correction; NOT USED IN FIT 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 (cih4omcalln.usen) are: Nabs ijk lmn A/2 Y3 Z3 X4 Y4 Z4 S ----- -=-==-= -------- -------- -------- -------- --------- --------- - 1 102 002 0.300000 0.000000 1.300000 0.000000 0.000000 2.300000 D 2 102 003 0.300000 0.000000 1.300000 0.000000 0.000000 2.700000 D 3 102 004 0.300000 0.000000 1.300000 0.000000 0.000000 3.050000 D 4 102 005 0.300000 0.000000 1.300000 0.000000 0.000000 3.400000 M and characters 73 through 132 of these six lines are: f(N) sumC*C Eex dEl34 dE(T) DTS |Ddc| DbasL Efinal --- ------- -------- ----- ----- ----- ----- ----- -------- .46 .976976 .441721 -34 4285 -739 1997 4961 .435080 .46 .974129 .340906 -137 3999 -751 2223 4750 .334356 .46 .977422 .322726 0 4791 -682 1745 4724 .316499 .30 .976481 .326959 -436 6160 -278 1766 4623 .321515 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 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; for H4, ijk is a 3-digit positive integer, and lmn is a 3-digit integer that may be negative. A/2 (F9.6) gives the position (in bohrs) of the first 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 shortest interatomic distance r12 between atoms 1 and 2. Y3,Z3 (2F9.6) give the position (in bohrs) of the third H-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)) give the position (in bohrs) of the fourth H-atom: x4 = X4 , y4 = Y4 , z4 = Z4 ; note that x4 is non-negative, r34 is never shorter than r12, but can be shorter than r23, and r14 and r24 can be shorter than r34 but are never shorter than r23. 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:H4 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 the additional small ad hoc corrections (in microhartrees); these comprise the ad hoc systematic correction to the extrapolation to zero threshold, and the ad hoc systematic correction to the open and mixed SCF-types. Omitting these small corrections has only a minor effect on the final energies: this can be accomplished by subtracting DTS from Efinal. |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-set 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 12 through 18, 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 through 5, the quantities S through |Ddc| refer to the best of the individual energy values from the corresponding files 12 through 16. Note that the quantites f(N) through |Ddc| (or their equivalents) were not in general available for the energies supplied by other authors. Meanings of the single-character type-code S (identifying the type of energy): ------------------------------------------------------------------------------ for H3 ab initio energies of other authors: ------------------------------------------- "S" = H3 ab initio energies using Slater-basis (linear geometries only), from B. Liu (1973), J. Chem. Phys., 58, 1925. "e" = H3 ab initio energies using the (9s3p1d)/[4s3p1d] basis set, from P. Siegbahn and B. Liu (1978), J. Chem. Phys., 68, 2457. "m" = H3 ab initio energies using the (9s3p1d)/[4s3p1d] basis set, from M. R. A. Blomberg and B. Liu (1985), J. Chem. Phys. (Notes), 82, 1050. "a" = H3 ab initio energies from C. W. Bauschlicher, S. R. Langhoff, and H. Partridge (1990), Chem. Phys. Lett., 170, 345. (Note that only a very approximate basis correction is available for these energies, as discussed in BKMP, and they were thus given very low weight in BKMP2.) "-" = H3 ab initio energies using the (11s5p3d1f)/[6s5p3d1f] basis set, from H. Partridge, C. W. Bauschlicher, J. R. Stallcop, and E. Levin (1993), J. Chem. Phys., 699, 5951. Note that a few additional and corrected energy values were supplied by H. Partridge (1994), private communication; the H2-basis-correction for this basis was supplied by H. Partridge (1992), private communication. for energies generated to constrain the H3 fit: ----------------------------------------------- "Z" = van der Waals region H3 energies computed from the modified Tang-Toenies (MTT) formulae fit to the data of Partridge et al. above (see BKMP2). "z" = the same as "Z", but with more extreme (large or small) values of r1. "t" = two H3 energy values generated from the saddle-point energy (and given high weight) to constrain the asymmetric-stretch and bending force constants, as was done by D. G. Truhlar and C. J. Horowitz (1978), J. Chem. Phys., 68, 2466; J. Chem. Phys. (Errata), 71, 1514 (1979). (Note that the first of these two energies requires seven decimal places of precision to set the force constant accurately enough, and thus has format F9.7 in the data file 1 [cih3allpts.usen].) "X" = very compact H3 energies generated from the London formula, to constrain extrapolation of the surface to short distances (i.e., high energies). for H4 ab initio energies of other authors: ------------------------------------------- "W" = H4 ab initio energies using the (8s2p1d)/[4s2p1d] basis set, from D. W. Schwenke (1988), J. Chem. Phys., 89, 2076, and D. W. Schwenke (1989), private communication. for energies generated to constrain the H4 fit: ----------------------------------------------- "K" = Schaefer & Kohler rigid-rotor van der Waals H2+H2 energies, for the equilibrium H2 size of 1.449 bohrs, with 45-degree angular grid. "k" = the same as "K", but with inermediate (22.5 degree) angular spacing. "F" = similar to "K", but with non=equilibrium H2-molecule sizes r1 & r2, using the modified Schaefer & Kohler surface (i.e., shifting R to match the ab initio repulsive wall smoothly, and reducing the anisotropic terms for small r1 or r2). "f" = the same as "F", but with more extreme variation of the sizes r1 & r2. "Y" = very compact H4 energies generated from the London formula, to constrain extrapolation of the surface to short distances (i.e., high energies). for our own H3 and H4 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 (3 or 4 open shells, for H3 or H4, respectively); otherwise same as above "b", "B", "h", "H" = molecular orbitals from mixed-shell SCF (1 closed shell, 1 or 2 open shells, for H3 or H4, respectively); 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 other type-codes (namely, "U", "n", and "R") are used to identify H4 energies of other authors; "g" is used to identify H3 van der Waals energies generated from the old Gengenbach formula (see BKMP paper), now superceded by the MTT formulae fit to Partridge energies (see BKMP2 paper and above). These type-codes are not found in any of the above files. 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.