A direct method for the location of the lowest energy point on a potential surface crossing

The model of the full optimized reaction space describes the electronic structure of a molecule in terms of the best wave-function that can be obtained as a superposition of all those configurations which are generate possible occupancies and couplings from a “formal minimal basis” of valence, orbitals on the constituent atoms. These configurations span a “full reaction space”, and MC SCF optimization of the orbitals in terms of an extended set of quantitative basis orbitals determines the full optimized reaction space (FORS). Basic justifications, methodological specifics and sample applications are discussed.

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

One of the classics in photochemistry, the photodimerization of anthracenes can be considered as a paradigm of the photocycloaddition of non saturated hydrocarbons. The historical steps of the mechanistic studies are reviewed: based on fluorescence quenching, cyclization quantum yields measurement, the influence of dioxygen and solvents, they support a singlet state pathway; the dimerization rate constants are found to be generally high for reactions occurring within a few nanoseconds unless they are slowed down or inhibited by steric strain. In several cases, excimers have been demonstrated to be intermediates and it is shown that excimer fluorescence and cyclization are competitive processes. Another intermediate known as pericyclic minimum (or conical intersection) is postulated to form a sort of floppy cycloadduct where the reacting centres are at mutual distances shorter than in excimers and longer than in dimers. For intermolecular dimerizations, the triplet state is also
reactive but through triplet–triplet annihilation in dilute solutions. Intramolecular photocycloadditions have also been carefully examined, for the role of multiple excimer formation, regioselectivity (9,10∶1′,4′ and 9,10∶1′,2′ cyclization) and solvent polarity. The triplet state reactivity is shown to lead to 4π + 2π or 4π + 4π cycloadducts, depending on geometric factors. In the latter case when intersystem crossing is favoured by the substituents, cyclization quantum yields as high as 0.65–0.72 have been observed. Photodissociation quantum yields are generally high and the reactions are partly adiabatic, leading to excimer and monomer fluorescence, but the major part follows another pathway not fully elucidated by flash photolysis. Thermodynamic and kinetic parameters for the thermal cleavage are given; they reveal a large gamut of stability for the photocycloadducts.

Photodimerization of anthracenes in fluid solutions: (part 2) mechanistic aspects of the photocycloaddition and of the photochemical and thermal cleavage

With the increasing availability of powerful computers, attempts to calculate the electronic structure and properties of molecules by the direct ab initio solution of a many-body Schrodinger equation have received a great stimulus. The authors review the mainstream developments in quantum chemistry and give a straightforward account of some of the many-body techniques borrowed, with appropriate modifications, from other areas of physics-field theory, nuclear theory and solid-state theory. After a historical introduction, the traditional approach based on the self-consistent field and the method of configuration interaction is developed in detail. This is followed by the introduction of the cluster expansion, various types of correlated electron-pair theory, and diagrammatic perturbation methods. Finally, propagator and Green function techniques are reviewed, not only as a means of calculating transition energies but also as an alternative approach to the determination of the electronic ground state.

http://iopscience.iop.org/article/10.1088/0034-4885/43/9/001/pdf

Quantum theory of molecular electronic structure

As the scope of quantum chemistry broadened from the consideration of stable molecules near equilibrium to encompass potential curves and surfaces, transition states, radicals, ions, and excited states, the shortcomings of the Hartree— Fock (HF) approximation for the description of the electronic structure of molecular systems became increasingly evident. The energy error of the restricted HF wave function, i.e., the difference between the HF limit energy (which is the limit approached by restricted self-consistent field calculations as the basis set approaches completeness) and the exact solution of the nonrelativistic Schrodinger equation, has been termed the correlation energy.(1) It reflects the fact that the HF Hamiltonian contains the average, rather than instantaneous, interelectron potential, and thus neglects the correlation between the motions of the electrons.

The Method of Configuration Interaction

Excited potential energy hypersurfaces for hydrogen (H4) at trapezoidal geometries. Relation to photochemical 2s + 2s processes

Excited potential energy hypersurfaces for H4. 2. "Triply right" (C2v) tetrahedral geometries. A possible relation to photochemical "cross-bonding" processes

Publisher Summary This chapter discusses matrix elements and density matrices for many-electron spin eigenstates built from orthonormal orbitals. For an important class of many-electron problems, namely, those governed by spin-free or nearly spin-free Hamiltonians, it is practically and theoretically useful to formulate many-electron wavefunctions that, in addition to being antisymmetric, are also eigenfunctions of the total spin operators. The most widespread method of constructing antisymmetric wavefunctions is by an expansion in terms of Slater determinants of orthonormal orbitals. Thereby quantum mechanical problems are transformed into matrix problems and the matrix elements are integrals involving two Slater determinants and certain dynamical operators. Slater determinants have, however, one shortcoming: In general, they are not eigenfunctions of the total spin operator. A second route can be considered as originating with Dirac's vector model. A third route is to construct spin eigenfunctions with the help of projection operators that are not derived from group theory. In all of these methods, the construction of wavefunctions with the desired characteristics is the simpler task. It is in the evaluation of the expectation values and matrix elements of the many-electron operators that complexities and complications arise.

Ronald D. Poshusta

Papers

Excited potential energy hypersurfaces for hydrogen (H4) at trapezoidal geometries. Relation to photochemical 2s + 2s processes

Excited potential energy hypersurfaces for H4. 2. "Triply right" (C2v) tetrahedral geometries. A possible relation to photochemical "cross-bonding" processes

Matrix Elements and Density Matrices for Many-Electron Spin Eigenstates Built from Orthonormal Orbitals

Hydrogen excimer - a bound state of h4