Excited State Electronic Structure Theory

The development of electronic structure theories for metal complexes has always been closely linked with electron spectroscopy of transition metal compounds. We shall in the following describe both DFT and wave function methods that have been used in the study of excited states. We shall also discuss their application to the tetroxo systems. 

---

Mi CO). The first metal-metal bond to be characterized (35) is the formally single Mn-Mn bond in Mi CO). This compound has often been used as the model for developing electronic structure theories (1.18.36.37). Extremely efficient photofragmentation is responsible for the structureless electronic spectrum and the lack of emission following excitation of this molecule. This spectroscopic deficiency necessitates photofragmentation studies to obtain data to verify theoretical models. Most of the photochemical experiments in the past explored the reactions of the lowest excited singlet state in the near ultraviolet. 

Figure 14. The absolute value of the average disrotatory angle as a function of time in femtoseconds. (The disrotatory angle is defined in the upper left inset.) Lower inset A onedimensional cut of the excited-state potential energy surface along the disrotatory and conrotatory coordinates. All other coordinates are kept at their ground-state equilibrium value, and the full and dashed lines correspond to two levels of electronic structure theory (see text for details). (Figure adapted from Ref. 216.)...

An important issue of the application of electronic structure theory to polyatomic systems is the selection of the appropriate basis set. As usual in quantum chemistry, a compromise between precision and computational cost has to be achieved. It is generally accepted that in order to obtain qualitatively correct theoretical results for valence excited states of polyatomic systems, a Gaussian basis set of at least double-zeta quality with polarization functions on all atoms (or at least on the heavy atoms) is necessary. For a correct description of Rydberg-type excited states, the basis set has to be augmented with additional diffuse Gaussian functions. Such basis sets were used in the calculations discussed below. 

There are other shortcomings in semiempirical TDDFT that are not related to the self interaction. Semiempirical TDDFT has the same overall formalism and algorithmic structure as TDHF and the energy distribution of excited-state roots from these methods is much less dense than the exact distribution from FCI. In other words, while TDDFT is formally an exact theory for excited states (cf. Runge-Gross theorem [2]), semiempirical TDDFT has only one-electron excitations just as TDHF or CIS, which are the crudest approximations in excited-state molecular orbital theory. 

The SAC/SAC-CI method is a correlated electronic-structure theory for the ground and excited states in various spin multiplicities. The SAC method belongs to the coupled-cluster theory [30, 31]. In the case of a closed-shell singlet state, the SAC wave function is written as... 

Till recently, computations of vibronic spectra have been limited to small systems or approximated approaches, mainly as a consequence of the difficulties to obtain accurate descriptions of excited electronic states of polyatomic molecules and to computational cost of full dimensional vibronic treatment. Recent developments in electronic structure theory for excited states within the time-dependent density functional theory (TD-DFT) and resolution-of-the-identity approximation of coupled cluster theory (R1-CC2) and in effective approaches to simulate electronic spectra have paved the route toward the simulation of spectra for significantly larger systems. 

Sudden polarization phenomenon was investigated in ethylene using nonempiri-cal molecular electronic structural theory [38]. The studies predicted that D2d symmetry of the ground state ethylene undergoes twisting in the excited state to attain a pyramidalized shape. 

For this study the density functional method was applied at its local approximation level. An application of the density functional to absorption and luminescence involves excited electronic states. As in any electronic structure theory, excited states are conceptually more difficult to treat than the ground state, since there is an orthogonality requirement with respect to all lower states. Despite the fact that DFT was originally designed to efficiently calculate electronic ground states, several extensions have been developed to treat excited states for a review see Jones and Gunnarsson [99]. 

Electronic excitation and ionization spectra have been widely used in various fields of molecular sciences and technologies. These spectroscopies provide useful information about the electronic structures of molecules. The electronic spectrum is sometimes called as molecular finger print and used for identification of molecules. The electronic-structure theory is necessary to understand and identify the electronic states involved... 

The SAC-CI method was proposed in 1978 as an accurate electronic-structure theory for the ground, excited, ionized and electron-attached states of atoms and molecules. The method has been successfully applied to various photochemistry involving more than 150 molecules and established to be a useful method for studying chemistry and physics involving various electronic states. In this article, we gave a brief overview of our SAC-CI applications to the molecular spectroscopy. 

Radford (1961, 1962) and Radford and Broida (1962) presented a complete theory of the Zeeman effect for diatomic molecules that included perturbation effects. This led to a series of detailed investigations of the CN B2E+ (v — 0) A2II (v = 10) perturbation in which many of the techniques of modern high-resolution molecular spectroscopy and analysis were first demonstrated anticrossing spectroscopy (Radford and Broida, 1962, 1963), microwave optical double resonance (Evenson, et at, 1964), excited-state hyperfine structure with perturbations (Radford, 1964), effect of perturbations on radiative lifetimes and on inter-electronic-state collisional energy transfer (Radford and Broida, 1963). A similarly complete treatment of the effect of a magnetic field on the CO a,3E+ A1 perturbation complex is reported by Sykora and Vidal (1998). The AS = 0 selection rule for the Zeeman Hamiltonian leads to important differences between the CN B2E+ A2II and CO a/3E+ A1 perturbation plus Zeeman examples, primarily in the absence in the latter case of interference effects between the Zeeman and intramolecular perturbation terms. 

---