Single-configuration Self-consistent-field Research Articles

Computed self-consistent field and singles and doubles configuration interaction spectroscopic data and dissociation energies for the diatomics B2, C2, N2, O2, F2, CN, CP, CS, PN, SiC, SiN, SiO, SiP, and their ions

Single configuration self-consistent field (SCF) calculations near the Hartree–Fock limit, and singles and doubles configuration-interaction (CI)(SDCI) calculations from this single SCF configuration have been performed for the ground and selected excited states of the molecules B2+, B2, C2+, C2, N2+, N2, O2+, O2, F2+, F2, CN, CN−, CP, CS, PN, SiC, SiC−, SiN, SiN−, SiO, and SiP. Potential energy curves, with Davidson corrections, have been obtained around equilibrium separations. Equilibrium bond lengths, vibrational energies, ionization potentials, and dissociation energies are reported.

Dipole moments in rare gas interactions

A hybrid model is used to calculate the dipole moments of care gas dimers and trimers. The exchange and polarization interactions are obtained with a single-configuration self-consistent-field (SCF) calculation and the dispersion contribution to the dipole is obtained by perturbation theory. The SCF dipoles for the trimers are found to compare well with values modeled by an exchange quadrupole-induced dipole mechanism. The dispersion dipole for the ArKr dimer is found to be significant compared to the exchange contribution even in the region of the equilibrium separation. Values of the B hyperpolarizability are evaluated for Ne, Ar, Kr, and Xe which allows the perturbation calculation of the dispersion dipole for any pair of rare gas atoms.

A New dimension to quantum chemistry: Theoretical methods for the analytic evaluation of first, second, and third derivatives of the molecular electronic energy with respect to nuclear coordinates

Perhaps even more important to quantum chemistry than enhancements in computer technology has been the theoretical development of analytical derivative methods. It may be realistically stated that such analytic derivative methods provide a new dimension to molecular electronic structure theory. The combination of the two effects (computational advances and theoretical progress) has led to explosive growth in the field. This account primarily describes theoretical developments at Berkeley over the past five years. Analytic first, second and third derivative methods have been developed for single-configuration self-consistent-field (SCF) wavefunctions. Analytic first and second derivative techniques now exist for multiconfiguration (MC) SCF and configuration interaction (CI) wavefunctions. These methods have been used to address a variety of chemical problems, some of which are described here.

Analytic energy derivative methods for excited singlet states of the same symmetry as the electronic ground state

The possibility of variational collapse of single configuration self-consistent field (SCF) wave functions for excited electronic states becomes more serious when first and second derivatives of the energy (with respect to nuclear coordinates) are required. For a nonlinear molecule of four or more nuclei, there will almost inevitably be some displacement which removes all spatial symmetry, leaving the electronic state in question with the same spatial symmetry as the ground electronic state. For excited singlet states, a resolution of this problem is found by using the Davidson–Stenkamp method to guarantee orthogonality to the closed-shell ground-state wave function. The Davidson–Stenkamp wave function is then transformed to a conventional two-configuration SCF wave function, to which analytic first and second derivative methods may be applied.

The cyclic, two-hydrogen bond form of the HO2 dimer

Among possible forms of the hydroperoxyl radical dimer H2O4, one of the most appealing and plausible is the six-membered ring 4. This cyclic isomer of H2O4 has been investigated using nonempirical molecular electronic structure theory. For the lowest triplet state of H2O4, the single configuration self-consistent field (SCF) method was used in conjunction with double zeta (DZ) and double zeta plus polarization (DZ+P) basis sets. At both levels of theory, the six-membered ring is predicted to be a minimum on the H2O4 potential energy hypersurface. The DZ SCF and DZ+P SCF dimerization energies are 4.5 and 4.9 kcal, respectively. Vibrational frequencies are predicted within the harmonic approximation and compared with the analogous monomer predictions and with the recent experimental findings of Diem, Tso, and Lee. It is concluded that the cyclic HO2 dimer is composed of two weak hydrogen bonds, each about one-half the strength of that observed for the water dimer.

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 reference function are found necessary to reduce the 2A2-2B1 separation to below 0.5 kcal.

A model transition metal-carbene system MnCH2

The first transition metal-methylene species, Ta(C5H5)2 CH3CH2, has recently been prepared and characterized by Schrock and co-workers. As a model for systems of this type, ab initio electronic structure theory has been applied to the MnCH2 molecule. After experimentation with several types of basis sets, the following double-zeta contracted gaussian basis was adopted: Mn(12s 8p 4d/8s 6p 2d), C(9s 5p/4s 2p), H(4s/2s). However, in some cases it was found necessary to add a set of more diffuse d functions to the above. Single-configuration self-consistent-field (SCF) potential curves are reported for electronic states dissociating to Mn+(4s 3d5 7S), Mn(4s2 3d5 6S), Mn(4s 3d6 6D) and Mn(4s 4p 3d5 8P) plus 3B1 CH2 and 1A1 CH2. The electronic ground state of MnCH2 is of 8B1 symmetry and for this state only a full geometry optimization was performed, yielding r e(Mn-C) = 2·16 A, θ e(HCH) = 109°, and r e(C-H) = 1·09 A. In the SCF approximation 8B1 MnCH2 is bound by 33 kcal/mole relative to infinitely separated 6...

Molecular theory of hyperfine pressure shifts in H caused by Ar and He buffers

The general applicability of molecular methods for studying hyperfine pressure shifts (HPS) in a hydrogen atom caused by Ar and He noble-gas buffers has been tested thoroughly by carrying out extensive multiconfigurational self-consistent-field (MCSCF) and single-configuration self-consistent-field (SCF) calculations on ArH and HeH diatomic systems. Calculations show that for a He atom, a light noble-gas buffer, single-configuration SCF molecular wave functions are sufficiently good in reproducing the HPS result quantitatively, although qualitatively the weak, long-range polarization features are not described. However, for a heavier noble-gas buffer, such as the Ar atom, the long-range polarization effects are the strong and dominant features in the ArH binary interaction. Because of a lack of a sufficient number of proper functions for describing the long-range polarization features, the single-configuration SCF molecular wave functions do not reproduce the long-range polarization effects adequately. For ArH, therefore, MCSCF molecular wave functions, constructed with a choice of configurations which describe the dominant polarizations, are employed to reproduce the HPS result quantitatively and the long-range features qualitatively. HPS results computed by using MCSCF molecular wave functions are in excellent agreement with the experimental result.

Potential energy surfaces for H + Li2 → LiH + Li ground state surface from large scale configuration interaction

A b initio electronic structure calculations have been performed to determine the HLi2 potential energy surface. A contracted Gaussian basis set was employed: H(5s 1p/3s 1p), Li(8s 3p/4s 3p). In addition to selfconsistent-field (SCF) wavefunctions, full configuration interaction (CI) was carried out for the three valence electrons. For general geometry (point group Cs), the CI included 5175 configurations. For the diatomic molecules Li2 and LiH, these methods yield dissociation energies within 5 kcal/mole of experiment, and accurate spectroscopic constants are also predicted. The minimum on the HLi2 CI potential surface occurs for an isosceles triangle structure with r (H–Li) = 1.72 Å and on LiHLi bond angle of 95°. This minimum lies 22.4 kcal/mole below the separated products LiH + Li. The linear HLiLi minimum is much shallower, lying only 4.2 kcal/mole below the products. The much simpler single configuration SCF calculations yield qualitatively similar results. Furthermore, these features of the surface are quite analogous to those predicted for F + Li2 by Pearson and coworkers. The angular dependence of the surface between the C2v and C∞v extremes is discussed. The ’’electron jump’’ from covalent HLi2 to ionic H−Li2+ is seen to be much more gradual than was the case for FLi2. The electronic structure is described using a natural orbital analysis of the most important configurations in the wavefunction.

Excited Electronic States ofO2−

Excited electronic states of the $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ molecule have been calculated with configuration-interaction (CI) variational trial functions that assure formally correct asymptotic behavior as well as the single-configuration self-consistent-field (SCF) approximation. CI results were obtained by both multiconfiguration self-consistent-field (MC-SCF) and pseudonatural orbital (PNO) techniques. The MC-SCF results are most accurate and are used to analyze the energy curves and wave functions of these states for internuclear separations larger than 3 a. u. All the excited states are found to have equilibrium-internuclear separations at least 1 a. u. larger than the ground state. The two lowest energy states, the $^{4}\ensuremath{\Sigma}_{u}^{\ensuremath{-}}$ and $^{2}\ensuremath{\Pi}_{u}$, are characterized, respectively, as shape and valence Feshbach resonances. They are sufficiently bound to make it likely they play a role in low-energy-electron scattering by oxygen.