William D. Laidig

Large multiconfiguration self‐consistent‐field wave functions for the ozone molecule

The electronic structure of the ozone molecule is of particular interest in light of Goddard’s characterization of the ground state as a biradical. Rigorously optimized multiconfiguration self‐consistent‐field (MCSCF) wave functions of varying size have been determined here for ozone via newly developed techniques utilizing the unitary group approach. The largest of these ab initio MCSCF wave functions includes 13 413 configurations, i.e., all singly‐ and doubly excited configurations relative to the two reference configurations required for the biradical description of ozone. The convergence of the MCSCF procedures is discussed, as well as the structure of the MCSCF wave functions, and the effectiveness of different orbital transformations. There is a significant energy difference (0.034 hartrees) between the MCSCF wave functions involving one and two reference configurations. This gives emphasis to the fact that orbital optimization alone cannot compensate for the exclusion from the wave function of imp...

Multiconfiguration self‐consistent‐field study of the importance of triply and quadruply excited electronic configurations in the water molecule

The importance of triple excitations, configurations differing by three electrons from the Hartree–Fock reference configuration, is of considerable interest in electronic structure theory. A simple double zeta basis set O(9s 5p/4s 2p), H(4s/2s) has been used to address this problem for the water molecule. Configuration interaction (CI) and multiconfiguration self‐consistent‐field (MCSCF) wave functions including up to all single, double, triple, and quadruple (SDTQ) excitations (a total of 17 678 1A1 configurations) have been obtained for this purpose. An interesting result is that the MCSCF wave function including only single excitations yields 52.3% of the comparable correlation energy obtained with all single and double excitations. Using canonical SCF orbitals, triple excitations are found to contribute only 0.8% of the correlation energy. However, the MCSCF procedure increases this correlation energy fraction by more than a factor of 5. The MCSCF energies for the wave functions including SD and SDTQ ...

Where to look for the electronic spectrum of hydrogen isocyanide, HNC

The geometrical structures and vibrational frequencies of the ground and first excited electronic states of HNC have been predicted by a priori theoretical methods. Using a standard double zeta plus polarization basis set, both the self‐consistent field (SCF) and configuration interaction with all single and double excitations (CISD) levels of theory have been employed. To allow a reasonable assessment of the reliability of the HNC theoretical predictions, analogous studies of the experimentally characterized HCN molecule are also reported. It is hoped that the HNC theoretical predictions will be of assistance in the identification of its electronic spectrum. The HNC electronic spectrum should be distinguishable from that observed by Herzberg and Innes for HCN by: (a) the prediction that the X 1Σ+–A 1A″ energy difference is ∼5000 cm−1 less for HNC than for HCN; (b) for HNC the upper state vibrational frequencies ν2 and ν3 are nearly equal (to within 100 cm−1), while for HCN, the C ≡ N stretch occurs mor...

Electronic symmetry breaking in polyatomic molecules. Multiconfiguration self‐consistent field study of the cyclopropenyl radical C3H3

For equilateral triangle geometries (point group D3h), the C3H3 radical has a degenerate 2E″ electronic ground state. Although the 2A2 and 2B1 components separate in energy for C2v geometries, these two components should have identical energies for equilateral triangle structures. In fact, when approximate wave functions are used and the orbitals not required to transform according to the D3h irreducible representations, an energy separation between the 2A2 and 2B1 components is observed. At the single configuration self‐consistent field (SCF) level of theory this separation is 2.8 kcal with a double‐zeta basis set and 2.4 kcal with double‐zeta plus polarization. It has been demonstrated that this spurious separation may be greatly reduced using multiconfiguration self‐consistent field (up to 7474 variationally optimum configurations) and configuration interaction (up to 60 685 space and spin adapted configurations) techniques. Configurations differing by three and four electrons from the Hartree–Fock ref...

Some characteristics of the intravalence triplet–triplet electronic transition in HCN

The precise theoretical predictions of the geometrical structures and relative energies of the two lowest triplet states of HCN are reported. (AIP)

New Directions for the Loop-Driven Graphical Unitary Group Approach: Analytic Gradients and an MCSCF Procedure

It is becoming increasingly apparent1–10 that the unitary group approach (UGA) provides the theoretical framework for an elegant and exceptionally efficient molecular calculus of quantum mechanical matrix element evaluation. Although this approach was pioneered by physicists primarily concerned with nuclear problems,11 it has more recently been demonstrated to be equally (perhaps more so) applicable to the many-electron problem. In our own research, a direct descendant of that of Paldus2,3 and Shavitt,4 the efficacy of the loop-driven 5,8 graphical UGA (LDGUGA) has been emphasized. In essence, the LDGUGA illuminates vast numbers of previously unrecognized relationships between different Hamiltonian matrix elements. Here we underline the generality of the LDGUGA formalism by establishing its applicability to two longstanding challenges to theoretical chemists. First, the determination of the two-particle density matrix provides a realistic approach to the problem of obtaining analytic energy gradients from correlated wave functions. Secondly, the LDGUGA holds promise for the determination of very large (on the order of 10,000 configurations) multiconfiguration self-consistent-field (MCSCF) wave functions.