Full CI Results Research Articles

Outer- and inner-valence ionization spectra of N 2 and CO: : SAC-CI (general-R) compared with full-CI spectra

The SAC-CI (symmetry-adapted-cluster configuration-interaction) (general-R) method describes the ionization and shake-up spectra of N 2 and CO in almost complete agreement with the full-CI results, though the computational labour of the former is much smaller that that of the latter. The SAC-CI (general-R) method is accurate for both valence and inner-valence regions of ionization spectra, while the SAC-CI (SD-R) method is good for the outer-valence region, but not always so for the shake-up region.

Properties of the correlated electronic states of pyrene and hydrogenated pyrene

Approximate calculations are reported on pyrene within the PPP model Hamiltonian using a novel restricted CI scheme which employs both molecular orbital and valence bond techniques. Also reported are detailed full CI results of the PPP model on 2,7-dihydropyrene obtained using the valence bond method. Spectral studies, charge and spin density calculations in ground and excited states, and ring current calculations in the ground state of the molecules are presented. In pyrene, the calculated excitation energies are in good agreement with experiment. The closed structure pi-conjugated molecule pyrene appears to show smaller distortions from the ground state geometry compared with the open structure pi-conjugated molecule 2,7-dihydropyrene. The ground state equilibrium structure of 2,7-dihydropyrene can be viewed as two hexatriene molecules connected by a vinyl crosslink, as is evident from bond order and ring current calculations. This is consistent with the only Kekule resonant structure possible for this molecule.

An iterative difference-dedicated configuration interaction. Proposal and test studies

An earlier work proposed a difference-dedicated configuration interaction method based on effective Hamiltonian arguments and was essentially devoted to the calculation of transition energies and binding energies. Using the resulting density matrices, the procedure may be made independent of the choice of starting molecular orbitals. This iterative redefinition of the MOs improves the quality of the results, as shown by comparing to full-CI results on CH 2, CH 2 + and SiH 2 vertical and adiabatic transition energies. The efficiency of the method for the treatment of weakly avoided crossings and for the determination of binding energies is illustrated on the LiF molecule. The mean deviation of the iterative difference-dedicated CI results to FCI energy differences is lower than 0.1 eV.

Hyperfine splitting constants studied by the symmetry adapted cluster-configuration interaction method

The accuracy of the symmetry adapted cluster-configuration interaction (SAC-CI) method for calculating hyperfine splitting constants (hfscs) is examined. Two kinds of SAC-CI expansion are performed: one is the SAC-CI(SD-R, DT-R) method in which single and double (double and triple for high-spin multiplicity) excitation operators are included in the linked operators and the other is the SAC-CI (general-R) method in which higher excitation operators are further included. The hfscs for the doublet, triplet, and quartet states of small radicals, OH, CH2, BH2, CH3, and H2O+, calculated by the SAC-CI method compare very well with the full CI results. A convenient configuration selection method, in which both energy and hfsc are used as criteria, is shown to be useful. This method, which is also applicable to the ordinary CI method, is effective for accurate calculations of the hfscs especially for large systems and high-spin systems, where a large number of configurations are required. Finally, the basis-set dependence of the hfscs is examined using the configuration selection method developed here. Within the Gaussian set, the improvement in energy does not necessarily result in the improvement of the hfscs. We have to use the basis set which satisfies the cusp condition, as shown previously.

Adding the linked contributions of Triples and Quadruples to a size-consistent Singles and Doubles CI

A convenient procedure has been proposed recently to insure the size-consistence of Singles and Doubles CI; the method goes through a self-consistent dressing of the energies of the excited determinants which incorporates the unlinked effects of the Triples and Quadruples. Two strategies are proposed here to add thelinked contributions of the Triples and Quadruples, either by an perturbative MP-type calculation of these effects, or by a redefinition of the dressing of the SD-CI matrix. Test calculations on Be2, FH, NH3 and F2 molecules show that both methods efficiently approach the Full CI results (error ∼ 1 kcal mol−1). The second one satisfactorily treats the single-bonds breaking. It is finally shown that the effect of the T-Q linked effects may be efficiently approximated by truncating the MO basis set to the most occupied virtual quasi-natural MOs.

Symmetry-adapted cluster–configuration interaction method applied to high-spin multiplicity

The SAC–CI (symmetry-adapted cluster–configuration interaction) method is extended to high-spin multiplicity and applied to the quartet, quintet, sixtet, and septet states of N2, N2+, OH, and m-phenylenebis(methylene) (m-PBM) molecules. The results show good agreement with those of the full-CI reference calculations, though the dimensions of the calculations are much smaller than those of the full-CI method. The smallness of the calculational efforts and the excellent agreement with the full-CI results assure that the SAC–CI method is useful and accurate not only for singlet, doublet, and triplet states but also for high-spin multiplet states.

Molecular application of the generalized symmetry adapted cluster theory

The generalized version of the symmetry adapted cluster theory (GSAC) which has been developed recently is nearly size-consistent and applicable to general classes of nonclosed-shell systems. The generality and the accuracy of the method have been tested for the symmetric dissociation of H 2O. The electron correlation energy and the excitation energy are compared with the full-CI results.

State-specific multireference Møller—Plesset perturbation treatment for singlet and triplet excited states, ionized states and electron attached states of H 2O

State-specific multireference Møller—Plesset perturbation theory has been applied to the study of electron correlations in the ground state, singlet and triplet excited states, ionized states and electron attached states of H 2O. The results compare well with SAC/SAC-CI and full-CI results. It is also shown that the same orbitals are, in principle, applicable to both ground and excited states of the neutral molecule and its ion simultaneously without redetermining orbitals for each individual state.

Multireference Møller—Plesset method

A multireference Møller—Plesset method is derived. The state-specific nondynamical correlation is accounted for by the MCSCF theory and the transferable dynamical correlation is estimated by the Møller—Plesset perturbation theory. There is a very close parallel between the standard single reference Møller—Plesset theory and the present multireference version. The method has been implemented at the second-order for 2-configuration MCSCF wavefunctions in which only two electrons are correlated. Potential curves for H 2, HF and F 2 molecules agree well with the full or near-full CI results.

Compact and accurate valence bond functions with different orbitals for different configurations: application to the two-configuration description of F 2

A way of computing reliable and very compact ab initio classical valence bond wavefunctions is presented. The method deals with a minimal number of configuration-state functions (CSFs), with only one per Lewis structure necessary to describe the active part of a chemical system since each CSF is allowed to have its specific set of orbitals, different from one CSF to the other. The coefficients of the CSFs and their orbitals, which remain purely local without any delocalization tails, are simultaneously optimized through a non-orthogonal MCSCF technique. The method is applied to the electronic structure of F 2. The wavefunction involves only two configurations, and yields a dissociation energy of 28.6 kcal/mol, which compares very well with the estimated full-CI result of 29–30 kcal/mol in an analogous basis set.

Approximating full configuration interaction with selected configuration interaction and perturbation theory

Selected configuration interaction (CI) calculations and second order perturbation theory are combined to systematically approach the full-CI limit. The resulting algorithm has negligible requirement for memory or disk space, being limited only by available cpu time. Comparison is made to existing full-CI benchmarks (DZ and DZP water, the oxygen atom and its anion, ammonia and the magnesium atom). In all cases the full-CI result is recovered to better than 0.1 kcal/mol.

Improved non-valence virtual orbitals for CI calculations

In order to improve the convergence of selected CIs it is crucial to define correlation-adapted virtual MOs. In the spirit of the frozen natural orbital method (diagonalization of the virtual MO block of the one-electron density matrix) the present paper proposes an inexpensive determination of that part of the density matrix to the Møller-Plesset second-order level. The superiority of the first eigenvectors of that matrix over the canonical MOs appears in their ability to concentrate significantly the correlation energy, as appears from test calculations on HF, H 2O, N 2, for which full CI results are available. The amount of correlation obtained from complete active space CIs involving one to five MOs is multiplied by a factor 1.5 to 2 in HF and H 2O. In selected CIs, using the CIPSI algorithm, the number of determinants required to obtain a given percent of the correlation energy is reduced by a factor from 2 to 5. The procedure may be applied with similar results after a preliminary definition of valence virtual MOs through CASSCF or more approximate procedures, concerning then only non-valence MOs and the dynamical correlation. Through this partition of the virtual subspace, perturbation divergences are avoided even for stretched bonds. The results on N 2 in a large basis set are specially convincing.

Triplet excitation properties in large scale multiconfiguration linear response calculations

It is shown that large scale MCSCF linear response (MCLR) calculations can be carried out efficiently when the perturbation operator has triplet symmetry. Methods have been developed to efficiently construct two electron density matrices containing triplet orbital excitation operators and two electron density matrices which connect singlet and triplet states. Direct CI methods have also been developed for two electron operators with spin rank one. Numerical calculations are presented for CH+ and the results compared with full CI results.

A potentially size-consistent multiconfiguration based coupled electron pair approximation

A coupled electron pair approximation is derived and illustrative calculations are presented. The present approximation, which we refer to as the unitary coupled electron pair approximation (UCEPA), provides multiconfigurational (MC) reference capability and is as computationally tractable as multireference configuration interaction (MRCI). The method is capable of yielding size-consistent energies if the MC reference function is of the complete active space (CAS) variety. The coefficient matrix of the resultant set of simultaneous linear equations is evaluated using internal/external orbital space partitioning within a unitary group approach (UGA) treatment of the state space. We demonstrate the accuracy of the method on several small benchmark molecules for which full CI results are known, and on nontrivial studies on the singlet–triplet splitting in methylene and the electron affinity of the oxygen atom.

A simple MC SCF perturbation theory: Orthogonal valence bond Møller-Plesset 2 (OVB MP2)

A multi-reference Møller-Plesset perturbation theory - orthogonal valence bond Møller-Plesset 2 (OVB MP2) - is derived using an effective Hamiltonian formalism. The method is characterized by the use of localized CAS SCF orbitals in order to achieve a quasi-degenerate (in terms of the one-electron reference Hamiltonian) reference space. Thus the reference CI expansion corresponds to orthogonal valence bond. The efficiency of the method is illustrated for two molecules (CH 2 3B 1 1A 1:H 2O r e, 1.5 r e, 2 r e) and the Be atom, where full CI results are available.

The dipole polarizability of Li −

We have calculated the lowest excitation energies and the static dipole polarizability of Li − as well as the electron affinity of Li using current quantum-chemical methods, including full CI. We have studied the convergence of the polarizability with the size of the orbital basis set. We find that electron correlation has a dramatic effect on the polarizability reducing it to roughly half its SCF value. MBPT calculations through fourth-order and perturbative propagator methods give an unsatisfactory description of the electron correlation whereas polarization propagator methods based on a coupled-cluster reference state give a polarizability in fair agreement with the full CI result.

Calculations on the electron affinity of silylene (SiH 2)

The electron affinity (EA) of SiH 2 was determined using various UHF-based methods with large basis sets (including f-functions). For purposes of comparison, the EA of Si and triplet-singlet separation in SiH 2 were also considered. The best calculations yield EA's of 1.37 and 1.00 eV for Si and SiH 2 respectively (experimental values are 1.385 and 1.124 eV). For the 3 B 1— 1 A 1, energy gap in SiH 2, comparison with available full CI results was also made. The best estimate for this quantity in the present work is 19.9 kcal mol −1 (expt. 21.0 ± 0.7 kcal mol −1).

Consistent generalization of the Møller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory

The Møller-Plesset partitioning of the many-electron Hamiltonian is generalized for arbitrary open-shell and multiconfigurational SCF reference states. The method has been initially implemented at the second and third orders for two-configuration generalized valence bond reference wavefunctions in which only two electrons are correlated. Potential curves for the hydrogen molecule, lithium hydride and the helium dication agree excellently with full CI results.

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

AbstractWithin the framework of the general extended geminal model, two new approximate models EXGEM4 and EXGEM5 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.

Full CI benchmark calculations on CH3

Full CI calculations have been performed on the CH3 radical. The full CI results are compared to those obtained using CASSCF/multireference CI and coupled-pair functional methods, both at the equilibrium CH distance and at geometries with the three CH bonds extended. In general, the performance of the approximate methods is similar to that observed in calculations on other molecules in which one or two bonds were stretched.