The optimization of MCSCF functions by application of the generalized brillouin theorem: The LiH2 potential energy surface

The generalized Brillouin theorem is used to construct an optimization procedure for MCSCF functions by iterative contracted CI calculations. Special attention is paid to the MO transformation step in each iteration. In this method the MCSCF calculation may easily be augmented by a restricted CI calculation involving a configuration set which is uniquely determined by the trial function. An application to the calculation of the potential energy surface for linear LiH₂ in the reaction LiH + HLi + H₂ leads to the conclusion that this restricted CI is necessary, in order to obtain satisfactory results for the potential energy barrier in this reaction.     

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.     

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.     

Direct minimization of the energy functional in the LCAO-MO density matrix formalism

A previously proposed method of energy minimization is developed for MC SCF wavefunctions formed by all-pair excitations for a closed-shell system. The orbital coefficients are optimized by a gradient approach using a suitable orthogonal transformation of the atomic basis, while optimum CI coefficients are determined solving the usual secular problem for the lowest eigenvalue, after each optimization of the orbitals. Applications to LiH and NH₃ molecules show that the method is numerically well stable, and is capable of accounting for a large part of the correlation energy giving results which compare well with those of the conventional CI method.     

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.     

Electronic properties of CH4 by CI computations

The total electronic energy and other quantities are calculated by a configuration interaction (CI) treatment, including all single and double excitations for CH₄, expanded over a large STO basis set. The correlation energy is not satisfactorily reproduced by such a basis set which is, however, able to give near Hartree-Fock (HF) results.     

Potential curves for dissociative electron attachment of CFCl3

Ab initio MRD CI potential curves are reported for CFCI₃ and CFCI₃ and the results are seen to give quantitative support to a recent interpretation of the dissociative electron attachment phenomenon in halocarbons, including the fact that in CFCl₃ itself such processes occur with essentially zero electron impact energies. Calculated vertical IP and transition energy results also found fit in quite well with corresponding measured values.     

Low-lying electronic states of Ben clusters (n = 7, 10, 13) and of the Be7H system

Self-consistent-field (SCF) calculations have been performed by means of a pseudopotential (PP) technique on medium-size Be_n clusters (n = 7, 10, 13). Correlation effects have been taken into account through multireference double-excitation configuration-interaction (MRD CI) procedure. Particular attention has been paid to the existence of Be clusters with many nearly degenerated states of singlet and triplet spin multiplicity. The SCF ordering of these states is frequently reversed in CI. Planar and non-planar Be clusters show comparable high stabilities caused by a strong sp hybridization. Two sections of the potential energy surface for the interaction of a H atom with the Be₇(7,0) cluster have been determined. Two regions of low energy found in this energy surface: one inside and the second outside the cluster border, are separated by an energy barrier. The CI results, indicating the directly overhead position as the absolute minimum of the surface, are in qualitative agreement with previous SCF studies on similar systems. The modifications of the cluster geometry (shrinkage or relaxation) caused by the interaction with the H atom in the directly overhead position are found to be very small.     

Spin-projected Extended Hartree-Fock using a Valence Bond approach

Summary We describe spin-projected Extended Hartree-Fock calculations, performed with a Valence Bond Self-Consistent Field program. Potential energy curves are given for BH, BeH, and N₂. For BH the EHF function ranks well with the corresponding Spin-coupled and full CI wave functions. For BeH, the EHF function introduces spin contamination in the separated Be atom due to the rigidity of the wave function. This results in an inferior potential energy curve compared to Spin-coupled and full CI. The triple bond breaking in N₂ is again nicely described by EHF. The Extended Hartree-Fock method as suggested by Löwdin can be a feasible tool in describing bond breaking.     

Correlation energies in open shell systems. Comparison of CEPA,PNO-CI and perturbation treatments based on the restricted Roothaan-Hartree-Fock formalism

A set of simple molecules in closed and open-shell ground states is treated by the three techniques mentioned in the title, using the same geometries and basis sets (DZ + P). It is found that for nearly all molecules treated in this study (exceptions are H₂ and CH₃) consistently about 98% of the CEPA valence shell correlation energy is obtained by third-order many-body Ray-leigh-Schrödinger perturbation theory (MB-RSPT). The CEPA and MB-RSPT results for reaction energies and barrier heights for some simple reactions differ by 0 to 30 kJ/mol, the CEPA results being in most cases closer to experiment than MB-RSPT, while CI results are much less reliable as long as CI is limited to singly and doubly substituted configurations only.     

A simplified method for molecular correlation energy calculations by separation into internal and non-internal parts. Application to multiconfigurational zeroth-order wavefunctions

A simplified method of determining the molecular correlation energy by two separate calculations, one for the internal and one for the non-internal correlation energies, is extended to multiconfigurational zeroth-order wavefunctions. This extension offers the possibility of deriving correlated potential energy curves or surfaces for processes involving configurational changes. The internal correlation energy is shown to be correctly determined by an MC/CI procedure combining the use of minimal and extended basis sets. An original semi-empirical “atoms-in-molecules” method based on the L.C.A.O. expansion of the molecular wavefunction is proposed for the non-internal correlation energy calculations. This method is shown to be able to overcome some of the shortcomings of a previous populations analysis approach. Test calculations concern potential curve parameters (D _e ,T _e ,R _e ,W _e ) of the ground and some excited states of the NH, C₂, HCN and CN molecules. The results are found to be in good agreement with corresponding experimental and large CI results. Aspirant du Fonds National Belge de la Recherche Scientifique Boursier I.R.S.I.A.     

Exploiting regularity in systematic sequences of wavefunctions which approach the full CI limit

Summary The ground state total energy and related 1-electron properties are computed for three small molecules (N₂, H₂O, and H₂CN) using several systematic sequences of wavefunctions which approach the full CI. These sequences include multireference CI, averaged coupled pair functional and quasidegenerate variational perturbation theory wavefunctions. It is demonstrated that sufficient regularity exists in the sequence of variationally computed energies to permit extrapolation to the full CI limit using simple analytic expressions. It is furthermore demonstrated that a subset of the original list of configurations employed in the normal singles and doubles CI procedure can be selected using second order perturbation theory without adversely affecting the extrapolation to the full CI limit. This significantly broadens the range of applicability of the method. Along these lines, a scheme is proposed for the extrapolation of the selected CI results to the zero threshold (i.e. unselected) values in cases where the numbers of configurations associated with the latter would render the calculations intractable. Due to the vast reduction in the number of configurations which are handled variationally, the proposed scheme makes it possible to derive estimates of the full CI limit in cases where explicit full CI is either very difficult or currently impossible.Dedicated to Prof. Klaus RuedenbergThe Pacific Northwest Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute under contract DE-AC06-76RLO 1830     

The generalized separated electron pair model. 1. An application to NH3

The utility of the separated electron pair (SEP ) model (strongly orthogonal geminals) is examined quantitatively, for pyramidal and planar nuclear configurations of the NH₃ molecule. The best SEP wave function computed for each species is capable of recovering about half of the correlation energy obtained by a fairly accurate configuration interaction (CI ) calculation, (corresponding to roughly 25% of the total molecular correlation energy). It is illustrated that the model can be systematically extended with only a modest effort to yield more accurate results (about 40% of the total correlation energy). The fact that the corrections to the SEP model have a simple physical interpretation suggests that this model may be a useful starting point for “brute force” CI calculations on larger chemical systems.     

Generalized-molecular-orbital theory: Simple multiconfiguration self-consistent-field method

Even after completing a multiconfiguration self-consistent-field (MCSCF ) calculation, one must often include additional configuration interaction (CI ) to obtain quantitative or semiquantitative results. There is some question of whether the prior MCSCF calculation is worthwhile, if additional CI is needed later. We have developed a new MCSCF computational method, which, because of our assumptions about the nature of the configurations, yields one Fock-like operator for all the “filled” orbitals (high occupation numbers) and a second Fock-like operator for all the “virtual” orbitals (low occupation numbers). Since there are only two matrices to build, our method is considerably faster than other MCSCF approaches. Because of these similarities to standard molecular-orbital (MO ) calculations, we have termed our approach generalized-molecular-orbital (GMO ) theory. However, the “virtual” orbitals, unlike those of standard MO theory, are optimized to correlate the “filled” ones and can he used in a subsequent CI calculation. Results are presented for the correlation energy of H₂O, the spectroscopic constants of N₂, the singlet–triplet energy separations in CH₂, and the nature of the chromium–chromium quadruple bond. Although these results are at a very low level of CI , the GMO approach appears to correct for the gross deficiencies of the single-determinant SCF procedure.     

Collisionally induced dissociation mass spectrometric studies of perfluorinated 1H-heptane,tert-butanol, 2-butyltetrahydrofuran and isopropyl bromobutyl ether

High-energy collision-activated dissociation in connection with mass-analyzed ion kinetic energy spectrometry (CAD/MIKES) was employed to probe the structures of some ions generated by methane chemical ionization (CI) and negative ion chemical ionization (NICI) of the title compounds. CAD/MIKES results show that the [M ? H]^? ion of lH-perfluorobeptane and the [O(CF₂)₄Br]^? ion of perfluoroisopropylbromobutyl ether are stable. The methane CI of these fluorocarbons also showed that the expulsion of HF molecules appears to be a major driving force for further fragmentations.     

Theoretical studies of photodissociation and rydbergization in the first triplet state (3s3A″2) of ammonia

Ab initio investigations at the RHF and CI levels have been carried out on a section of the potential energy surface of the Rydberg 3s³A″₂ state of NH₃ leading to dissociation into NH₂(²B₁) and H(²S). It was found that the barrier towards dissociation is due to a Rydberg-valence transformation. The barrier height calculated with the CI wavefunction is significantly smaller than at the RHF level The results may explain the difficulties associated with experimental observation of the 3s³A″₂ state.     

Radial limit of lithium revisited

Configuration interaction (CI) calculations are carried out for the ground state of lithium using a thoroughly optimized basis set of s-type Slater functions. They establish that the radial limit of the nonrelativistic energy of the ground ²S state of lithium is no higher than −7.448666443E_h. Thus, radial correlation accounts for 35.2% of the total correlation energy. The radial CI wave function predicts a significantly more accurate Fermi contact parameter than the Hartree-Fock wave function. However, the imbalanced treatment of electron correlation in the radial CI wave function leads to an excessively diffuse electron density that is worse than that of the Hartree-Fock wave function. © 1997 John Wiley & Sons, Inc.     

Generalization of analytic energy derivatives for configuration interaction wave functions

This paper takes the form of a review including some original contributions. A fresh derivation of analytic energy derivative expressions for configuration interaction (CI) wave functions is presented. In this method the CI energy is described by _IJC_IC_J(H _IJ-_IJE) so that the orthonormality condition is explicitly included therein. In the sequence of differentiations up to fourth order it will be demonstrated that each derivative may be expressed in terms of (H _IJ-_IJE) and its derivatives in a symmetric way with respect to the interchange of differential variables. In a similar manner, the CI variational condition may be described in an equation which explicitly includes the normalization condition. It is shown that the differentiation of the modified variational condition produces the coupled perturbed configuration interaction (CPCI) equations in directly soluble and compact forms. The necessary formulae for the energy derivatives up to fourth order and the CPCI equations up to second order are explicitly given.     

Structure of Mn2(CO)10 and Mn2(CO)9: Insights from ab initio calculations

Optimization of the Mn–Mn distance in Mn₂(CO)₁₀ with various basis sets of at least doublezeta quality results in Mn–Mn bond lengths in the range of 3.07–3.15 Å, 0.2–0.25 Å longer than the experimental value of 2.895 Å. Incrementing the basis set with diffuse p functions (exponent 0.0332) on the carbon atoms improves the calculated bond length to a value of 2.876 Å at the CI level, as a consequence of a charge transfer between each Mn atom and the equatorial carbonyls of the other Mn atom. For Mn₂(CO)₉ four structures have been studied at the SCF and CI levels with assumed geometries. The structure with a symmetric bridging carbonyl turns to be much higher in energy at the SCF level. The two structures which are purely metal–metal bonded [corresponding to the departure of an axial or equatorial carbonyl from Mn₂(CO)₁₀] are nearly degenerate in energy and more stable than the structure with a semibridging carbonyl by 5 kcal/mol at the SCF level and 10–11 kcal/mol at the CI level (seemingly at variance with the conclusions of matrix experiments that favor the semibridging structure).