Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Moller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is, applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. The independent electron-pair approximation is accurate to second order in a Moller-Plesset expansion, but inaccurate in third order. A series of variational methods is discussed which gives upper bounds for the energy, but which lacks size consistency. Finally, calculations on some small molecules using a moderately large Gaussian basis are presented to illustrate these points. Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are describe substantially better by Moller--Plesset theory to second or third order than by Hartree--Fock theory.

Theoretical models incorporating electron correlation

The ab initio multiple spawning (AIMS) method is a time-dependent formulation of quantum chemistry, whereby the nuclear dynamics and electronic structure problems are solved simultaneously. Quantum mechanical effects in the nuclear dynamics are included, especially the nonadiabatic effects which are crucial in modeling dynamics on multiple electronic states. The AIMS method makes it possible to describe photochemistry from first principles molecular dynamics, with no empirical parameters. We describe the method and present the application to two molecules of interest in organic photochemistryethylene and cyclobutene. We show that the photodynamics of ethylene involves both covalent and ionic electronic excited states and the return to the ground state proceeds through a pyramidalized geometry. For the photoinduced ring opening of cyclobutene, we show that the disrotatory motion predicted by the Woodward−Hoffmann rules is established within the first 50 fs after optical excitation.

Ab Initio Multiple Spawning: Photochemistry from First Principles Quantum Molecular Dynamics

Multireference Møller-Plesset method

The multiconfiguration self-consistent field (MCSCF) method offers the most general approach to the computation of chemical reactions and multiple electronic states. This review discusses the design of MCSCF wavefunctions for treating these problems and the interpretation of the resulting orbitals and configurations. In particular, localized orbitals are convenient both for selection of the appropriate active space and for understanding the computed results. The computational procedures for optimizing these wavefunctions and the techniques for recovery of dynamical correlation energy are reviewed.

The construction and interpretation of MCSCF wavefunctions.

Generalized valence bond description of bonding in low-lying states of molecules

A priori quantum mechanical calculations have been carried out at about 150 linear geometries for the fluorine plus hydrogen molecule system An extended basis set of Gaussian functions was used, and electron correlation was treated explicitly by configuration interaction Comparison with the experimental activation energy and exothermicity suggests that the theoretical potential surface is quite realistic

https://science.sciencemag.org/content/sci/176/4042/1412.full.pdf

Potential Energy Surface Including Electron Correlation for F + H2 → FH + H: Refined Linear Surface

Theoretical studies are reported of the complete dipole excitation and ionization spectrum in H_2O employing Franck–Condon and static‐exchange approximations. Large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground‐state equilibrium geometry, and previously devised moment‐theory techniques are employed in constructing the continuum oscillator‐strength densities from the calculated spectra. Detailed comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact–excitation cross sections, and dipole (e, 2e)/(e, e+ion) and synchrotron‐radiation studies of partial‐channel photoionization cross sections. The various calculated excitation series in the outer‐valence (1b(^−1)_1, 3a(^−1)_1, 1b(^−1)_2) region are found to include contributions from valence‐like 2b_2 (σ*) and 4a_1(γ*) virtual orbitals, as well as appropriate nsa_1, npa_1, nda_1, npb_1, npb_2, ndb_1, ndb_2, and nda_2 Rydberg states. Transition energies and intensities in the ∼7 to 19 eV interval obtained from the present studies are seen to be in excellent agreement with the measured photoabsorption cross section, and to provide a basis for detailed spectral assignments. The calculated (1b(^−1)_1)X(^ 2)B_1, (3a_1(^−1))^2A_1, and (1b_2(^−1))(^2)B_2 partial‐channel cross sections are found to be largely atomic‐like and dominated by 2p→kd components, although the 2b_2(σ*) orbital gives rise to resonance‐like contributions just above threshold in the 3a_1→kb_2 and 1b_2→kb_2 channels. It is suggested that the latter transition couples with the underlying 1b_1→kb_1 channel, accounting for a prominent feature in the recent high‐resolution synchrotron‐radiation measurements. When this feature is taken into account, the calculations of the three outer‐valence channels are in excellent accord with recent synchrotron‐radiation and dipole (e, 2e) photoionization cross‐sectional measurements. The calculated inner‐valence (2a_1(^−1)) cross section is also in excellent agreement with corresponding measured values, although proper account must be taken of the appropriate final‐state configuration‐mixing effects that give rise to a modest failure of the Koopmans approximation, and to the observed broad PES band, in this case. Finally, the origins of the various spectral features present in the measured 1a_1 oxygen K‐edge electron energy‐loss profile in H_2O are seen to be clarified fully by the present calculations.

/pdf/theoretical-studies-of-photoexcitation-and-ionization-in-h2o-2xr1rnd9ca.pdf

Theoretical studies of photoexcitation and ionization in H2O

Theoretical investigations of photoexcitation and ionization cross sections in molecular nitrogen are reported employing the recently devised Stieltjes–Tchebycheff moment-theory technique in the static-exchange approximation. The coupled-channel equations for photoabsorption are separated approximately by identifying the important physically distinct excitation processes associated with formation of the three lowest electronic states of the parent molecular ion. Approximate Rydberg series and pseudospectra of transition frequencies and oscillator strengths are constructed for the seven individual channel components identified using Hartree–Fock ionic core functions and normalizable Gaussian orbitals to describe the photoexcited and ejected electrons. Detailed comparisons of the theoretically determined discrete excitation series with available spectral data indicate general accord between the calculated and observed excitation frequencies and oscillator strengths, although there are some discrepancies and certain Rydberg series have apparently not yet been identified in the measured spectra. The total Stieltjes–Tchebycheff vertical photoionization cross section obtained from the discrete pseudospectra is in excellent agreement with recent electron–ion coincidence measurement of the cross section for parent–ion production from threshold to 50 eV excitation energy. Similarly, the calculated vertical partial cross sections for the production of the three lowest electronic states in the parent molecular ion are in excellent accord with the results of recent electron–electron coincidence and synchrotron–radiation branching ratio measurements. The origins of particularly intense resonancelike features in the discrete and continuum portions of the photoabsorption cross sections are discussed in terms of excitations into valencelike molecular orbitals. Small discrepancies between theory and experiment are attributed to specific autoionization processes and channel couplings not included in the calculations. In contrast to previously reported model or local potential studies, the present results employ the full nonlocal and nonspherical molecular Fock potential in ab initio photoabsorption calculations. The excellent agreement obtained between theory and experiment in molecular nitrogen suggests that highly reliable photoabsorption cross sections for diatomic molecules can be obtained from Hilbert space calculations and the Stieltjes–Tchebycheff method in the static-exchange approximation under appropriate conditions.

/pdf/photoabsorption-in-molecular-nitrogen-a-moment-analysis-of-4u3zkwvlv4.pdf

Photoabsorption in molecular nitrogen: A moment analysis of discrete‐basis‐set calculations in the static‐exchange approximation

Theoretical assignments of the low-lying electronic states of carbon dioxide

/pdf/a-critical-test-of-semiempirical-fh2-potential-energy-2mf231bywy.pdf

Charles F. Bender

Papers

Potential Energy Surface Including Electron Correlation for F + H2 → FH + H: Refined Linear Surface

Theoretical studies of photoexcitation and ionization in H2O

Photoabsorption in molecular nitrogen: A moment analysis of discrete‐basis‐set calculations in the static‐exchange approximation

Theoretical assignments of the low-lying electronic states of carbon dioxide

A critical test of semiempirical FH2 potential energy sufaces: The barrier height for H + FH → HF + H