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SCF and CI Studies on Ground State of Water Molecule Ab initio SCF and CI studies on the ground state of the water molecule. II. Potential energy and property surfaces Bruce J. Rosenberg, Walter C. Ermler, and Isaiah Shavitt Citation: J. Chem. Phys. 65, 4072 (1976); doi: 10.1063/1.432861 View online: http://dx.doi.org/10.1063/1.432861 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v65/i10 Published by the American Institute of Physics. Additional information on J. Chem. Phys. Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors Downloaded 29 Apr 2013 to 134.76.213.205. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions Ab initio SCF and CI studies on the ground state of the water molecule. II. Potential energy and property surfaces Bruce J. Rosenberg* and Walter C. Ermlert Department of Chemistry. The Ohio State University. Columbus. Ohio 43210 Isaiah Shavitt Department of Chemistry. The Ohio State University. Columbus. Ohio 43210 and Battelle Memorial Institute. Columbus. Ohio 43201 (Received 29 June 1976) Self-consistent field and configuration interaction calculations for the energy and one-electron properties of the ground state of the water molecule were carried out with a (5s4p2d/3s1p) 39-function STO basis set. The CI treatment included all single and double excitation configurations (SD) relative to the SCF configuration. and a simple formula due to Davidson was used to estimate the energy contribution of quadruple excitations and thus produce a set of corrected (SDQ) energies. The calculations were carried out for 36 molecular geometries (22 symmetric and 14 asymmetric) in the neighborhood of the equilibrium geometry. Least-squares analysis was used to determine theoretical equilibrium geometries and to derive quartic and cubic expansions for the energy and one-electron properties in terms of internal displacement coordinates. Considerable improvement was found in the SD and particularly in the SDQ results relative to SCF. with the SDQ equilibrium geometry being in excellent agreement with experiment and the harmonic force constants also showing much better agreement than other ab initio results. Results for higher-order force constants are difficult to assess because of the large uncertainties in both theoretical and experimental results. The dipole moment function obtained in these calculations should be quite useful in the assessment and analysis of infrared intensity data and isotope effects. I. INTRODUCTION Rz =Ro + l6R, (1) This paper is the second in a series concerned with e=iJo+mM, the use of self-consistent field (SCF) and configuration where Rl and R are the two OH bond lengths, iJ is the interaction (cI) calculations for describing and analyz­ z bond angle, Ro= 1. 811096 bohr (0.958390 A), iJo ing the electronic and vibrational structure of the water = 104. 44992°, 6R = O. 03 bohr (0.015875 A), oiJ = 3 0, and molecule in its ground electronic state. Paper I of this k, i, m =0, ± 1, ± 2. The central point (k = 1= m = 0) is series1 presented a comparison of several contracted the geometry used in Paper I and by several other Gaussian-type (CGTO) and Slater-type (STO) basis sets authors, while the step sizes 6R and 6iJ are the same as in terms of computed SCF and CI energies and one­ those used in earlier studies of the H 0 potential sur­ electron properties of the molecule at one geometry 2 face, Z.3 and correspond to one third to one quarter of very near the experimental equilibrium geometry. The the root-mean-square zero-point vibrational amplitudes best results were obtained with a basis set of 39 Slater­ of the molecule. 5 Of the possible combinations of k, i, type orbitals, which gave an SCF energy within 0.003 m in the indicated range (- 2 '" k, i, m ",2), only the 21 hartree of the estimated Hartree-Fock limit and a CI symmetric geometries (k = l) for which I k I + I m I '" 3 and energy which accounts for 75% of the estimated correla­ the 14 asymmetric points for which either - 1 '" k, i, m tion energy. This basis set (denoted 39-STO) has been '" 1 or m =0 and I k + II '" 2 were used. (Because of used in the present study to calculate potential energy symmetry it was sufficient to consider only those pOints and property surfaces for the ground state in the neigh­ for which I k I "Ill.) The 36th point was the interpolated borhood of the equilibrium geometry at both the SCF and minimum obtained from a quartiC polynomial least­ CI levels. Quartic and cubic polynomials in terms of squares fit to the CI energies of the first 35 points. (No displacement coordinates, derived by least-squares calculations were carried out at the interpolated mini­ fitting to computed property values, have been used to mum of the SCF potential surface.) The geometries and represent the results. computed energies for all 36 points are given in Table I. A forthcoming paper will present vibrational analyses of the SCF and CI potential energy and property surfaces The calculations carried out at each of the 36 points based on a perturbation theory formalism that includes used the 39-STO (5s4p2d/3s1p) basis set, 1.6 and in­ the effect of anharmonicity. Z-4 cluded SC F and CI wavefunctions, energies, and one­ electron operator expectation values, as described for II. CALCULATIONS point 1 in Paper I. The CI calculations (designated by the symbol SD in the following) included all single and Electronic wavefunctions and properties were calcu­ double excitations relative to the SCF configuration, lated at 36 pOints on the potential surface. Of these, using the canonical SCF occupied and virtual orbitals 35 points were generated by the formulas at each point. This involved 4120 configuration func­ Rl =Ro+k6R, tions (CF's) for the symmetric (Cav) geometries and 4072 The Journal of Chemical Physics. Vol. 65, No. 10. 15 November 1976 Copyright © 1976 American Institute of Physics Downloaded 29 Apr 2013 to 134.76.213.205. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jcp.aip.org/about/rights_and_permissions Rosenberg, Ermler, and Shavitt: Ground state of water molecule. II 4073 TABLE I. Potential energy surface of the water molecule from tained by means of the POLYCAL programs, 7 while the CI SCF and CI calculations, using a 39-STO (5s4p2d/3s1p) basis calculations were carried out with programs developed set. a at Battelle Memorial Institute and The Ohio State Uni­ versity, as described in Paper I. The SCF coefficients Geometryb Energy, c -(E+76) Point and CI density matrices obtained for aU points are No. k m SCF available in a technical report. B 1 000 0.06422577 0.33980247 0.3547926 2 o 0 1 0.06414298 0.33961279 0.3545784 Since the energy differences between neighboring 3 o 0-1 0.06381601 0.33952631 0.3545451 points were generally of the order of several hundred 4 1 1 0 0.06256213 0.33899141 0.3542622 microhartrees, and since the coefficients in a quartic 5 -1 -1 0 0.06489634 0.33963488 0.3543528 6 1 1 0.06239286 0.33870841 0.3539520 polynomial fit to the surface depend on fourth differ­ 7 1 1-1 0.06224509 0.33881457 0.3541158 ences, it was important to assure high preCision, of the 8 -1 -1 0.06490378 0.33954215 0.3542371 order of 1 J-Lhartree or better, in the individual ener­ 9 -1 -1 -1 0.06439010 0.33925574 0.3540002 gies. This was accomplished by tightening the accuracy 10 002 0.06359281 0.33898092 0.3539254 tolerances in the basis set integral calculations (to 11 o 0-2 0.06289035 0.33876205 0.3538139 12 220 0.06000885 0.33730488 0.3528640 better than 0.1 J-Lhartree) and in the convergence of the 13 -2 -2 0 0.06445973 0.33837471 0.3528284 SCF and CI wavefunction calculations. The fact that the 14 1 0 0 0.063392-1"1 0.33939464 0.3545249 computed potential surfaces were smooth and substan­ 15 -1 0 0 0.06455959 0.33971641 0.3545702 tially free from random errors was confirmed by the 16 1 -1 0 0.06372334 0.33930400 0.3542976 17 1 -1 1 0.06363925 0.33911313 0.3540816 small magnitudes of the least-squares deviations in 18 1 -1 -1 0.06331505 0.33902921 0.3540515 fitting the results to quartic polynomials, as described 19 200 0.06211138 0.33854437 0.3538181 in the next section. 20 -2 0 0 0.06433688 0.33907962 0.3538004 21 2 -1 0 0.06243928 0.33844911 0.3535857 The need for high preciSion and freedom from random 22 -2 1 0 0.06349768 0.33866267 0.3535228 errors ruled out the use of configuration selection 23 2 -2 0 0.06221064 0.33780319 0.3528060 schemes to reduce the computational effort of the CI 24 1 1 2 0.06176162 0.33798841 0.3532094 25 -1 -1 2 0.06443821 0.33900174 0.3536777 treatment, though one series of calculations was car­ 26 1 1-2 0.06141913 0.33815623 0.3534925 ried out to assess the effect of freezing the oxygen 27 -1 -1 -2 0.06336092 0.33838182 0.3531571 inner-shell electrons (such an SD-FC calculation! would 28 2 2 1 0.05975677 0.33693209 0.3524623 reduce the number of CF's for the symmetric points 29 2 2-1 0.05978076 0.33722366 0.3528158 30 -2 -2 1 0.06456100 0.33838238 0.3528151 from 4120 to 2587, and would reduce the computational 31 -2 -2 -1 0.06385328 0.33788902 0.3523672 effort in the CI stage by about a factor of 2).
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