Sten Rettrup

An iterative method for calculating several of the extreme eigensolutions of large real non-symmetric matrices

Abstract A new method is described for calculating several of the extreme eigensolutions of large real non-symmetric matrices. The matrices considered are assumed to have real eigenvectors and eigenvaluesw. An algorithm is presented for both single and multiple vector optimization. The efficiency of the two versions are compared using some test calculations. The method is a generalization of the Davidson-approach.

Limited configuration interaction calculation of the optical spectrum for the permanganate ion

Abstract A series of limited configuration interaction calculations based upon an extended basis set is presented for the permanganate ion. The configurations have been selected so that they describe initial and final states equally well, and the size of the expansion has been increased until a reasonable convergence in the results has been assured. Both singlet and triplet states have been treated. Electron density changes occurring at the so-called charge-transfer transitions have been studied, and relaxation turns out to play an important role. The agreement with experimental spectra is satisfactory.

Benchmarking Second Order Methods for the Calculation of Vertical Electronic Excitation Energies: Valence and Rydberg States in Polycyclic Aromatic Hydrocarbons †

The performance of the six second order linear response methods RPA(D), SOPPA, SOPPA(CCSD), CIS(D), CC2, and CCSD, which include either noniterative or iterative doubles contributions, has been studied in calculations of vertical excitation energies. The benchmark set consisted of 39 valence and 76 Rydberg states of benzene and five polycyclic aromatic hydrocarbons. As reference values we have used the results of the corresponding calculations with the third order method CCSDR(3), which includes noniterative triples contributions. In addition we have also carried out equivalent calculations at the level of the random phase approximation as well as with the configuration interaction singles and multireference configuration interaction singles and doubles methods.

Two-photon absorption cross sections: An investigation of the accuracy of calculated absolute and relative values

We have studied the basis set and electron correlation effects on the ab initio calculations of two-photon absorption cross sections of water. Various series of correlation consistent basis sets up to triply augmented basis sets of valence pentuple zeta level as well as the popular 6-31G(d) basis set have been employed in combination with several coupled cluster, configuration interaction, and density functional theory methods. We find that it is very difficult to obtain converged values of the cross sections for even a small molecule such as water. Acknowledging these difficulties in obtaining a fully converged cross section for a given state, we also investigated the possibility of determining relative cross sections for a series of organic molecules. However, we did not find consistency between the relative cross sections calculated at the Hartree-Fock level and several coupled-cluster methods using the 6-31G(d) and aug-cc-pVDZ basis sets. However, we could reproduce the relative ordering of the two-photon absorption cross sections of the molecules studied at the Hartree-Fock level.

Group Theoretical Techniques and the Many-Electron Problem

Publisher Summary This chapter studies many-electron systems using tensor bases for the irreps of the unitary group. Various ways of enumerating the basis states of the unitary group have been discussed. Procedures for calculation of configuration interaction (CI) matrix elements have been described. The discussion of the basis states of irreps of U (n) is general enough so as to be easily extendable to any many-fermion system, although applications have been restricted to the study of many-electron systems. The construction of angular momentum states for multishell configurations of electron in atoms, described in this chapter, could equally well be used for isospin-free nuclear shell model studies in the j–j coupling scheme. The chapter also discusses that generalization of these ideas to wave functions constructed from nonorthogonal single-particle states is straightforward and leads to the study of irreps of GL (n). This study has been carried out using one parameter alternant molecular orbital basis in a CI-calculation on some molecules.

Hartree–Fock operators to improve virtual orbitals and configuration interaction energies

The definitions of Hartree–Fock operators able to provide virtual orbitals more suited for correlation and excited electronic states and for configuration interaction (CI) treatments have been reviewed. From the comparisons, a simple procedure to improve these operators has emerged and discussed. In our approach, the sign of the pair and total electronic densities is changed to make the interelectron potential attractive for excited electrons. The orbitals generated from the modified operators have been compared to canonical HF orbitals by performing large scale CI computations on ground and excited states of the NO+ molecule improving the CI energies and the dipole moments for all states and the convergence properties of CI. Similarly, using truncated orbital subspaces, the ground state MP2 correlation energy becomes closer to the basis limit for this property.

EFFICIENT TRUNCATION STRATEGIES FOR MULTI-REFERENCE CONFIGURATION INTERACTION MOLECULAR ENERGIES AND PROPERTIES

Modified virtual orbitals are proposed for multi-reference configuration interaction (MRCI) treatments and a modified Fock operator is defined for the orbital transformation. The main property of the modified orbitals is to improve the convergence properties of the configuration interaction (CI) expansion, which can be exploited to truncate, partially, the expansion in the external space. Simple tests are presented to show that the orbital transformation may be useful to perform FullCI type of treatments for subsets of orbitals and electrons, and to improve the MRCI second-order corrections and energies. Compared to other well-established techniques for accurate MRCI treatments, it is believed that this method offers advantages for electronic structures with many active orbitals and electrons using large orbital basis sets.

Ab initio configuration interaction study of the Rydberg states of the hydroxymethyl radical CH2OH

Abstract The ultraviolet absorption spectrum of the hydroxy methyl radical has been studied by ab initio configuration interaction methods using a large Gaussian-type basis set. The first four vertical electronic transition energies have been calculated to be at 287, 243, 221 and 219 nm. Dipole moments are presented for all the states together with the oscillator strengths for the transitions. A detailed analysis of the orbitals shows that the transitions are of Rydberg type which can be classified as π→3s, π→3p x , π→3p y and π→3p z .

A configuration interaction (CI) procedure for the evaluation of two‐photon electronic transition probabilities. Program implementation with application to the A1g→B2u transition of benzene

A CI program is described for the evaluation of two‐photon electronic transitions, based on time dependent second order perturbation theory. The expression of the transition amplitudes is obtained by directly solving first order perturbation equations over the CI components, avoiding the second order expression with summation over the full set of the intermediate CI eigenstates. The procedure has been implemented as part of a general CI program for ab initio computations of these properties. To test the program, the relative intensities of the ‘‘hot’’ vibronic components of the A1g→B2u transition of the benzene molecule have been evaluated on a minicomputer and compared to the experiment.

A permutation‐group direct configuration interaction procedure for second order molecular properties. Program implementation with application to the A 2Σ+←X 2Π two‐photon transition of the OH radical

A permutation group direct configuration interaction program, using graphical techniques, has been extended to second order properties. Using this program, absolute and relative two‐photon cross sections have been evaluated for the rotational lines of three vibronic bands 0–0, 1–0, 1–1 of the A 2Σ+←X 2Π transition of OH. The computed absorption coefficients are compared with the available experimental data.