Accuracy of first-order wavefunctions for ten-electron atomic systems

It is demonstrated that for Ne-like systems, the zeroth-plus-first-order wavefunctions, obtained within Rayleigh—Schrödinger perturbation theory based on H₀ = H_HF, are of the same accuracy as variational wavefunctions obtained in CI calculations using very extensive sets of singly and doubly excited configurations. Variational correlation energies for Na⁺, Mg²⁺ and Ar⁸⁺ are reported for the first time.     

Iterative natural orbitals for configuration interaction using perturbation theory

Approximate natural orbitals are determined iteratively from CI expansions constructed using first-order perturbation theory in order to investigate the possibility of eliminating the complete transformation of MO integrals on each iteration. Results on LiH and H₂O are compared with fully variationally determined NO's to assess questions of convergence.     

Static dipole polarizability of electronically excited molecules: H2(B1Σu+)

The dipole polarizability of H₂(B¹Σ_u⁺) is computed using extended Gaussian basis sets and Hartree-Fock, multiconfiguration Hartree-Fock, and configuration interaction wavefunctions. Electron correlation contributions are found to be significant (≈ 25%) with the largest contribution arising from angular correlation. With a full CI wavefunction, the components of the dipole polarizability were computed to be (in au): α_⊥ = 50 and α_| = 257.     

Deadwood in configuration spaces. II. Singles + doubles and singles + doubles + triples + quadruples spaces

The effect of truncating singles + doubles configuration interaction (CISD) and singles + doubles + triples + quadruples (CISDTQ) spaces on the energies of the systems Ne, H₂O, CO and C₂ is investigated through the use of a previously described, general, selected CI program. CI expansions generated by Hartree–Fock orbitals as well as by natural orbitals are examined and the latter typically exhibit faster convergence as regards the energy. For the CISD wavefunctions of Ne, H₂O, CO and C₂, chemical accuracy is reached by using, respectively, 34, 47, 53 and 55% of the full sets. For the triples + quadruples parts of the wavefunctions on the other hand, chemical accuracy is already reached by using only 1, 4, 6 and 9% of the respective full sets. Received: 14 August 2001 / Accepted: 6 December 2001 / Published online: 8 April 2002     

Electron momentum spectroscopy of the valence orbitals of H2O and D2O: Quantitative comparisons using Hartree—Fock limit and correlated wavefunctions

The large discrepancies found earlier between experimental measurements and calculations based on near Hartree—Fock wavefunctions for the valence orbital electron momentum distributions of H₂O are reinvestigated. New and improved electron momentum spectroscopy measurements for the valence orbitals of H₂O and D₂O, together with existing experimental data, have been placed on a common intensity scale using the binding energy spectra. Investigation of possible vibrational effects by means of new measurements of the momentum distributions of D₂O indicates no detectable differences with the H₂O results, within experimental error. A quantitative comparison of these experimental results with both the shapes and magnitudes of momentum distributions calculated in the PWIA and THFA approximations using new, very precise Hartree—Fock (single-configuration) wavefunctions is made. These wavefunctions, which include considerable polarization and which are effectively converged at the HF limit for total energy, dipole moment and momentum distribution permit establishment of basis set independence. The significant discrepancies between theory and experiment which still remain for the momentum distributions of the 1b₁, 3a₁ and 2a₁ orbitals at the THFA level are largely removed by CI calculations of the full ion—neutral overlap amplitude. These CI wavefunctions for the final ion and neutral ground states, generated from the accurate HF limit basis sets, recover up to 88% of the correlation energy. The present work clearly shows the need for adequate consideration of electron correlation effects in describing the low-momentum parts of the 1b₁, 3a₁ and 2a₁ electron distributions, a region which is of crucial importance in problems related to chemical bonding and reactivity. The high level of quantitative agreement obtained between experiment and calculations using sufficiently sophisticated wavefunctions provides support for the essential validity of the plane wave impulse approximation as used in the interpretation of EMS experiments on small molecules.     

Accurate ab intio determination of binding energies for rare-gas dimers by basis set extrapolation

To investigate the electron correlation effect on the binding energies of very weakly bound complexes at highly correlated levels, an extrapolation scheme exploiting the convergent behavior of the binding energy differences between two correlation levels with the correlation-consistent basis set aug-cc-pVXZ was explored. The scheme is based on extrapolating the binding energy differences between the lower and higher correlation levels (such as second-order Møller–Plesset perturbation theory and the single and double coupled-cluster method with perturbative triple correction level), CCSD(T), by X^–3 for relatively small basis set calculations to estimate the corresponding basis set limit, which is then added to the complete basis set(CBS) limit binding energy at the lower correlation level to derive the CBS limit binding energy at the higher level. Test results on rare-gas dimers Rg₂ (Rg is He, Ne, Ar) show that the CCSD(T) CBS limit binding energies estimated by this scheme with aug-cc-pVXZ and aug-cc-pV(X+1)Z basis sets are more accurate than the CBS limit estimated by direct extrapolation of correlation energies by X^–3 with aug-cc-pV(X+1)Z and aug-cc-pV(X+2)Z basis sets in most cases, which signifies the utility of the proposed extrapolation scheme as the level of electron correlation treatment increases. The nonnegligible discrepancy in the well depth near equilibrium between the experimental and the full connected single, double, and triple coupled-cluster method CBS limit estimate obtained by this procedure in the case of Ar₂ suggests that the previous semiempirical potential may be too attractive near equilibrium compared with the actual one.Acknowledgement The major portion of this work was carried out while the author was visiting the Quantum Theory Project (QTP) at the University of Florida. The author is thankful to Rodney Bartlett for hospitality and support during the visit. The author is also thankful to Ajith Perera for assistance in using the ACESII program package. Computational support from the QTP at the University of Florida and the Institute for Basic Science at Ajou University is gratefully acknowledged.     

Theoretical investigations on the solvation process

STO double-zeta SCF wavefunctions for various configurations of the H₅O ₂ ⁺ associate have been computed. Results are discussed and compared with other authors' similar calculations on gaussian bases.An electrostatic picture of the monosolvation of H₃O⁺ is proposed as a fairly satisfactory one.     

Cumulative BK approximation as a method to select configurations for CI calculations of transition energies

A cumulative B_k approximation is examined as a method to select configurations for CI calculations of transition energies where all the matrix elements are computed (full CI). The results obtained by this approach indicate that the transition energies are comparable to the ones obtained at the full CI level. Even for truncation errors of 1 mhartree, the transition energies differ from the full CI ones by less than 0.1 eV.     

SCF MO CI perturbation calculations of inner shell and valence shell vertical ionization potentials

A CI method for calculating inner and valence shell vertical ionization potentials is presented. It is based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for the ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest. The state energy is computed by performing a CI calculation for a set of selected configurations, and then adding the contributions of the remaining configurations as estimated by second order Brillouin-Wigner perturbation theory. The use of the same set of MO's for all states together with the CI perturbation method makes the method rather rapid. The numerical results are, in spite of the limited Gaussian basis sets used, in good agreement with experiment.     

Multireference perturbation CI I. Extrapolation procedures with CAS or selected zero-order spaces

We discuss the “three class” approximation to full multireference perturbation CI, which greatly reduces the computational effort by restricting the summation of diagrams to determinants belonging to a subspace of the zero-order space. In the framework of the CIPSI algorithm, we propose a new extrapolation procedure allowing recovery of the full “two class” results. The new procedure is applied to complete active spaces (CAS) and to individually selected zero-order spaces. Comparison with a full two class calculation on a CAS shows a reduction of computer time of one or two orders of magnitude in the tests presented here, with an accuracy in the order of 0.1 kcal/mol. Our procedure can thus compete with the CASPT2 algorithm, specifically conceived to deal with CAS. In the case of selected zero-order spaces, the speed-up is less dramatic but the method still retains its advantages. Received: 12 June 1997 / Accepted: 31 July 1997     

Dynamic correlation for biorthogonal valence bond reference states

Summary The use of biorthogonal valence bond reference functions in evaluating the correlation energy is investigated. Since the method is not variationally bound some care must be taken in defining the reference state to ensure that the variational bound is not violated, some discussion is given to this matter. The procedure adopted here is a matrix element driven configuration interaction scheme. To reduce the computational labour involved, a configuration selection criterion is introduced. The method is tested through its application to the symmetric stretching of HF, H₂O, (² B ₁) NH₂ and the singlet-triplet gap in CH₂. Comparison is made with other methods, including full CI. The results show that the current method is quite promising.     

Full CI benchmark calculations for molecular properties

Full CI calculations of first- and second-order properties are presented to provide benchmark results for comparisons with other methods, such as multireference CI(MRCI). The full CI(FCI) polarizability of F^– is computed using a double zeta plus polarization plus diffuse basis set. These FCI results are compared to those obtained at other levels of theory; the CASSCF/MRCI with Davidson correction results are in excellent agreement with the FCI. Differences between the polarizability results computed as a (numerical) second derivative of the energy or as an induced dipole moment are also discussed. FCI calculations are presented for the dipole moment and polarizability of HF, CH₂ and SiH₂ using a DZP basis set. Again, the CASSCF/MRCI values are in excellent agreement with the FCI results, whereas SDCI values, whether computed as an expectation value or as an energy derivative, are much worse. The results obtained using the CPF approach are in considerably better agreement with the FCI results than SDCI, and are similar in quality to the SDCI energy derivative results with the inclusion of Davidson's correction.     

Identification of deadwood in configuration spaces through general direct configuration interaction

 In order to identify ineffective and, hence, superfluous configurations in algorithmically generated configuration spaces, a direct configuration interaction (CI) method has been developed for determining completely general configurational expansions based on arbitrary determinantal configuration lists. While based on the determinantal ordering scheme of Knowles and Handy, our direct CI algorithm differs from previous ones by the use of the Slater–Condon expressions in direct conjunction with single and double replacements. A full, as well as a completely general selected, CI program has been implemented. With it, full configuration spaces of Ne, C₂, CO and H₂O with up to about 40 million determinants have been investigated. It has been found that, in all cases, fewer than 1% of the configurations in a natural-orbital-based configuration expansion reproduce the exact results within chemical accuracy. Received: 19 December 2000 / Accepted: 9 May 2001 / Published online: 11 October 2001     

Accuracy of energy extrapolation in multireference configuration interaction calculations

The accuracy of extrapolation procedures in conjunction with energy-based configuration selection in CI calculations is examined. The normally high accuracy of such extrapolation can deteriorate in multireference CI calculations when configuration functions of low weight are included in the root (reference) set. This is due to the inadequacy of second-order energy contribution estimates for the very large number of discarded low-contribution functions generated as single and double excitations from the minor members of the root set. The problem may be overcome by increasing the number of configurations included in the zero-order function used for the energy contribution estimation process. Illustrative results are presented for excited states of the H₂O molecule and the H₂O⁺ ion.     

AB initio calculation of the zero-field splittings of the X3Σg− and B3Πg,i states of the S2 molecule

The zero-field splitting of the ³Σ_g^? ground state of S₂ is computed employing MRD CI wavefunctions obtained in a series of AO basis sets. All one- and two-electron spin—orbit interactions are included in the theoretical treatment and results are obtained and compared using second-order perturbation theory techniques and a CI-type diagonalization procedure. The computed data are found to be in good agreement with experiment, including the dependence of the splitting parameter on vibrational quantum number, and are seen to be quite stable with respect to variations in the AO basis as well as the number of inner-shell core orbitals maintained doubly occupied in all Slater determinants employed in the theoretical treatment.     

Quantum chemical study of the geometries and stabilities of the two valence-tautomers of C2H2F+

Non-empirical SCF-MO molecular wavefunctions were computed for the two limiting structures of C₂H₂F⁺ with full geometry optimization using double-zeta quality atomic orbital basis sets. The bridged structure (fluorenium ion) was found to be an energy maximum (transition state) about 31 kcal/mole higher than the open structure (fluoro-vinyl cation). The latter, contrary to the unsubstituted vinyl cation, is slightly (4.5 °) bent away from fluorine at the electron deficient centre.     

Full CI calibration of model hamiltonian,large basis set studies of the H2-H2 van der Waals interaction.

The non-variational CEPA2 PNO ansatz, recently employed in detailed studies of the H₂-H₂ van der Waals interaction by Burton and Senff and the full CI extrapolation studies on the same system by Burton are discussed in relation to the explicit full CI study of Harrison and Handy for the planar T configuration of H₂-H₂ (R = 6.5 a_o) in a basis of 80 functions.     

The ground state of the CN+ ion: a multi-reference Ci study

An extensive configuration-interaction study employing an AO basis including f polarization functions is undertaken for the ¹Σ⁺ and ³Π states of the CN⁺ ion at their respective equilibrium geometries. The importance of a multi-reference set for configuration generation is thereby exemplified in detail; all calculations in which the reference configurations contribute more than 90^~c to the final CI vectors (and similar amounts to both states) place the ¹Σ⁺ state lower than ³Π by ΔE_e = 0.10–0.20 eV at all stages. i.e. for a selected (large) subset, after extrapolation to the entire MRD CI space of up to 176000 configurations, and also at the estimated full CI level of treatment.     

A multi-configuration reference CEPA method based on pair natural orbitals

Summary A multi-reference CI scheme is proposed which is aiming at a considerable reduction of the generally very large number of configurations of CI expansions in multi-configuration reference cases. This reduction is achieved by combining the idea of internal contraction, the concept of pair natural orbitals (PNO's) and CEPA (coupled electron pair) type approximations for the contributions of higher than double excitations. This latter estimate leads to size consistent results and also permits to employ reference wavefunctions that contain only the dominantly occupied configurations of the considered system. Applications to two test cases, the lowest states (³ P,¹ D and¹ S) of the carbon atom and the symmetry forbiddenC _2v insertion reaction of Be and H₂, show that our method is able to truncate CI expansions to lengths of no more than 10³–10⁴ without losing more than 1–2% of the correlation energy. The calculated excitation energies and energy barriers agree with the full CI results in the respective basis within about 1 kcal/mol. Thus the MC-CEPA-PNO method presents a very efficient way to obtain chemical accuracy in CI-calculations for molecular systems.Dedicated to Prof. Dr. W. Kutzelnigg on the occasion of his 60th birthday     

Relative stability of the 3A2, 1A2, and 1A1 states of phenylnitrene: A difference-dedicated configuration interaction calculation

The relative stability of the ³A₂, ¹A₂, and ¹A₁ states of phenylnitrene is evaluated by means of ab initio calculations followed by difference-dedicated configuration interaction (DDCI). This approach is based on effective Hamiltonian theory at a low order of perturbation to select rationally the determinants which contribute to the energy difference. The CI space built on this criterion is then treated variationally. The method allows a considerable reduction of the CI space compared with a complete CAS*SDCI calculation (where CAS stands for complete active space). Depending on the concerned energy difference, different model spaces may be chosen, as illustrated in the ³A₂ → ¹A₂ and the ³A₂ → ¹A₁ transitions in phenylnitrene. Since the CI space may reach considerable dimensions, a direct CI algorithm for selected CI spaces, the SCIEL algorithm, has been used to perform the calculations. The results are in excellent agreement with previous calculations and with available experimental data. © 1996 by John Wiley & Sons, Inc.