Ab initio SCF and MRD CI studies of the FHCl− ion

The equilibrium geometry and hydrogen-bonding energy of the heterobihalide ion FHCl^? have been calculated by ab initio SCF and MRD CI methods using an AO basis set of near Hartree-Fock quality. In the most stable (linear) conformation of this ion, the equilibrium F Cl/FH distances are predicted to be 5.657/1.754, 5.453/L800 and 5.437/1.801 bohr by SCF, MRD CI and full CI (estimated) calculations respectively. A second minimum, which is of extremely small depth and corresponds to the hydrogen atom near the chlorine atom, begins to appear in the potential surface at an FCl distance of about 6.0 bohr. The hydrogen-bonding energy of FHCl^? lies in the range 18–22 kcal/mol.     

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.     

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.     

Individualized configuration selection in CI calculations with subsequent energy extrapolation

A configuration selection method for CI calculations is discussed and applied in which the energy lowering produced in a secular equation by the addition of a given test species to a series of dominant configurations is used as an ordering parameter. Configurations with energy lowerings below a given energy cut-off value are not included in the final secular equations but instead a method of estimating the combined effect of the neglected species on the corresponding non-selected CI results is developed. The influence of the choice of main configurations used in the selection process is given close examination as well as the importance of the MO basis employed in the treatment as a whole; in the latter case a non-iterative procedure for obtaining approximate natural orbitals for such calculations is suggested. The resulting configuration selection procedure is equally applicable to all types of electronic states in any nuclear geometry and the results of the associated CI calculations are seen to be essentially equivalent to a complete treatment in which all single- and double-excitation species with respect to aseries of dominant configurations in a given state are included. Senior U.S. Scientist Awardee of the Alexander von Humboldt Foundation, on leave from the Department of Chemistry, University of Nebraska.     

A systematic CI procedure with modified virtual orbitals

The use of modified virtual orbitals is studied in a systematic conventional CI procedure which offers considerable potential in regard to convergence and extension to larger systems. The method is applied to the HCN molecule by using 37 basis functions, and analysis of energy expectation values, together with the one-electron density, yields some insight into the physical content of CI wavefunctions.     

Potential energy curves for the X1∑ g, B1△g and B''''1∑ g states of C2 using MRCI and approximate CI methods

The potential energy curves for the X1∑ g, B1△g and B′1∑ g states of C2 have been studied by using MRCI and approximate CI methods, and are benchmarked against the calculations of full configuration interaction (FCI). The results obtained by MRCI method agree with the FCI very well, and even are accurate enough to compare other approximate methods as benchmark, when the calculations of FCI are not feasible. The approximate CI methods mentioned in this paper are reliable for treating chemical problems.     

Multireference configuration interaction treatment of potential energy surfaces: symmetric dissociation of H2O in a double-zeta basis

Multiconfiguration SCF and multireference CI calculations have been performed for the H₂O molecule in a double-zeta basis for four symmetric geometries, for comparison with full CI results. Unlike single-reference results, the energy errors are almost independent of geometry, allowing unbiased treatments of potential energy surfaces.     

Electron correlation described by extended geminal models: The EXGEM2 and EXGEM3 models

The general extended geminal model is reviewed and two new approximate models EXGEM 2 and EXGEM 3 are introduced. In a test calculation on water using a double-zeta basis set, the approximate models recover 93.4% of the full CI correlation energy defined within the same basis set. A test calculation on the neon atom demonstrates that the performance of the models in comparison with the full CI , will improve as the basis set is increased. It is suggested that for basis sets of moderate and large size, and which include polarization functions, the extended geminal models are likely to recover 95%–97% of the correlation energy obtainable by the full CI .     

Limited GSMO CI and ESMO CI study of electronic transitions in FNO

Limited CI calculations of vertical excitation energies and oscillator strengths have been performed in the ground state molecular orbital basis set (GSMO) and the excited state ones (ESMO). The absorption and emission spectrum of FNO is rediscussed on the basis of these calculations. The relaxation energy of excited states and the convergence of the CI expansion in the GSMO and ESMO basis sets is discussed.     

Analytical first derivatives of the energy for small CI expansions

Using the Z-vector formalism the analytical gradient of the energy in small CI expansions is derived and implemented for semiempirical MNDO-type methods. The computation time is shown to scale as O(N ³) with the size of the system, with the memory requirements growing as O(N ²). The evaluation of the analytical gradient is significantly faster than the underlying SCF and CI calculations, so that routine full geometry optimizations at the semiempirical CI level become possible for large systems. Received: 24 April 1997 / Accepted: 10 June 1997     

MRD CI study of the photodissociation of HO2 into OH(X2II) + O(3P, 1D)

A MRD CI procedure has been used to calculate several electronic states of the hydroperoxyl radical. The basis set is of double-zeta plus polarization quality augmented with s- and p-type bond and Rydberg functions. The vertical excitation energies of the lowest eight doublet and six quartet states are reported. Oscillator strengths for transitions form the ground to upper doublet states were calculated. A cut of the potential energy surfaces along the OOH fragmentation pathway is used to discuss the mechanisms of HO₂ photodissociation below 6.4 eV. Arguments are presented which indicate O(¹D) rather than O(³P) is the primary dissociation product, and so support the experimental findings rather than theory in the conflict raised earlier on this matter. Ostensibly the dissociation proceeds diabatically on the surface of the initially populated ²A″(1a″ → 2a″) state yielding OH(X²II) + O(¹D).     

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     

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.     

The externally contracted CI method applied to N2

An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ? functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ? functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a ¹Π_g and B ³Π_gstates caused by spin–orbit interaction with the ⁵Σ_g⁺ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.     

Comparisons of the RPA,SCRPA, Tamm–Dancoff,and full CI methods by analysis of their transition density matrices,oscillator strengths,and energy moments of oscillator strengths for the electric dipole transitions from the ground state of the B+ ion (frozen K-shell model)

The RPA, SCRPA , Tamm–Dancoff, and full CI methods are compared by analyzing their transition density matrices, oscillator strengths, and energy moments of oscillator strengths for the ¹S_ground – ¹P_odd transitions of the 4-electron B⁺ ion in the frozen K-shell approximation. It is found that the RPA gives transition density matrices that are aligned nearly as well as possible along those of the full CI , but have vector lengths that are significantly too long. The corresponding transition energies are significantly too small. These errors compensate to give oscillator strengths for the dominant transition that, for all forms of the oscillator strength, are within 1.6% of the corresponding full CI values. The SCRPA gives better transition density matrices than the RPA , but poorer oscillator strengths. The Tamm-Dancoff approximation gives very good values for the mixed length-velocity form of the oscillator strength. The RPA gives a static electric dipole polarizability that is nearly 20% larger than that of the full CI . The SCRPA gives a value 15% smaller than—and the Tamm-Dancoff approximation gives a mixed length-velocity value that is 11% larger than—that of the full CI . Other energy moments of oscillator strengths are also reported. Certain other approximations related to the RPA and the SCRPA are reported as well.     

Perturbative virtual SCF CI treatment for energy levels of coupled oscillator systems

A perturbative SCF CI treatment to obtain energy levels of coupled oscillator systems is proposed. The method uses the virtual SCF basis set, and the SCF equations are solved by means of a perturbative treatment that provides the diagonal matrix elements involved in the CI calculation. The off-diagonal matrix elements are calculated using a commutation relationship derived from exact quantum theorems. Numerical results for several systems are obtained and compared with those from others SCF, SCF CI , and variational treatments.     

Intermolecular interactions. Potential energy curves for H2-H2 system in two different MO basis sets

In a frozen CI basis two MO basis sets have been studied, an SCF MO and an orthogonal localized molecular orbital (OL MO) one. It is expected to reproduce the potential energy curve calculated by means of an SCF MO CI procedure with an OL MO CI which is less time consuming and more easily interpreted than the former. The quantitative reproduction is not satisfactory; nevertheless numerical results show that one is still able to get qualitative information. In both procedures all integrals have been considered and calculated on a gaussian basis.     

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.     

Electron correlation described by extended geminal models: The EXGEM4 and EXGEM5 models

Within the framework of the general extended geminal model, two new approximate models EXGEM 4 and EXGEM 5 are introduced. The models are tested against full CI calculations on the water molecule for three different nuclear configurations and a full CI potential energy curve for the LiH molecule in the ground state. On the basis of these calculations, it is suggested that the models will yield electronic correlation energies with an accuracy of 1–2% of the corresponding full CI result.