Excited state, molecular orbital

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 selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

An acronym for highest occupied molecular orbital. In a photochemically excited state, this orbital is represented as HOMO, (p. 693)... 

The fairly strong coupling which persists in the excited state between the excited electron and the electron with which it was paired in the ground state molecular orbital prior to excitation accounts for the stability of the complex. 

Table 3. Treatment of the n7t (A2), 7C7t (Ai) excited states of formaldehyde using various Cl methods (Buenker-Peyerimhoff Morokuma-Hayes ), Whitten-Hackmeyer 3 ) based on the ground-state molecular orbitals (GSMO s)...

Oxygen plays an important role in hydrolysis processes of both the transition and the even series elements. The formation of polycompounds such as polyphosphates, silicates etc. is due to contribution of the excited state d-orbitals in the molecular orbitals arising,... 

Like its neutral parent molecule, the NFg ion is a regular pyramid with Cgv symmetry. A single vacancy 6a in the doubly occupied highest molecular orbital 6ai of neutral NFg gives the ground term A [4]. Some excited states with orbital vacancies 5e la 4e 5a and 3e" are known from photoelectron spectra of NFg, see p. 185. 

Diels-Alder reaction involves /i, j/2, V3 and ]/4 orbitals of 1, 3-butadiene andrt and71 orbitals of ethylene as reactants m.os andCj, CT2,7t, 7i, a3,04 orbitals of cyclohexene which are product molecular orbitals. When these molecular orbitals are arranged in the increasing order of their energies alongwith their symmetries, ground state molecular orbitals of reactants correlate with the ground state molecular orbitals of their product, therefore, reaction is thermally allowed but photochemically forbidden on account of the fact that first excited state of reactant does not correlates with first excited state of product (Fig. 5.6). 

Configuration state functions (spin-adapted Slater determinants) constructed from excitation-adapted molecular orbitals (EAMOs) possess minimal off-diagonal elements of the Hamiltonian matrix. These orbitals, which result from separate unitary transformations among the occupied and virtual MOs. offer the most concise description of electronic excited states in terms of electron jumps . For example, at the CIS/6-31 +G level of theory, a symmetric combination of Just two singly excited configurations built from EAMOs [0.7049(7 — 9) -I-0.7049(6 -> 8)] suffices to adequately describe the first triplet excited state of N2, whereas several configurations involving MOs [0.5975 (7 9) -I- 0.5975(6 8) -t- 0.3646(7 16) -l-0.3646(6 15) -I- 0.0858(7 23) -I- 0.0858(6 22)J are... 

The first applications of natural orbitals were the factorization of the two electron wave function of He and H2. Iterative natural orbitals were used to develop accurate wave functions for many small molecules in ground and excited states. Natural orbitals provide a powerful tool for reducing wave functions expanded using an arbitrary set of molecular orbitals to a more compact canonical form that shows rapid convergence. Used in this way, they are a useful interpretive tool. 

Pericyclic reactions require an energy source, which can be either thermal or photochemical. Pericyclic reactions are thermal if they only require heat for the conversion of one or more reactants into product. The temperature need not be high some thermal pericyclic reactions occur at room temperature. The common feature of thermal pericychc reactions is the transformation of ground state molecular orbitals of the reactant into the ground state molecular orbitals of the product. Pericyclic reactions are photochemical if they requite hght for the conversion of one or more reactants into product. Photochemical pericychc reactions occur when a reactant absorbs hght to form an electronically excited state. Thus, the mechanisms of thermal and photochemical pericyclic reactions differ because they involve different molecular orbitals as well as different energy sources. 

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