Excitation valence

The simplest description of an excited state is the orbital picture where one electron has been moved from an occupied to an unoccupied orbital, i.e. an S-type determinant as illustrated in Figure 4.1. The lowest level of theory for a qualitative description of excited states is therefore a Cl including only the singly excited determinants, denoted CIS. CIS gives wave functions of roughly HF quality for excited states, since no orbital optimization is involved. For valence excited states, for example those arising from excitations between rr-orbitals in an unsaturated system, this may be a reasonable description. There are, however, normally also quite low-lying states which essentially correspond to a double excitation, and those require at least inclusion of the doubles as well, i.e. CISD. 

The lowest Bj and A2 excited states of C3H2 correspond to valence excitations from the Ipc... 

Electronic states and photodissociation dynamics of chloromethyl radical have been studied recently.114-117 Because of the chlorine substitution, there are several low-lying valence excited states (such as l2Ai and 22Bi, which mainly involve the orbitals on the CC1 bond) in addition to the 3s Rydberg state (22Ai), and more dissociation channels are available. 

Eq 7 calculates the energy difference arising from the medium between the thermally equilibrated mixed-valence ground state and a vibrationally nonequilibrium, mixed-valence excited state. The value of Ae depends on the nonequilibrium state 1) For optical charge transfer, Ae = e, the unit electron charge. 2) For thermal electron transfer between chemically symmetrical sites, Ae = e/4. 3) For a chemically unsymmetrical electron transfer... 

In order to understand the origin of the breakdown of the SR methods away from equilibrium, consider the torsional potential in ethylene (Figure 2). While at its equilibrium geometry ethylene is a well-behaved closed-shell molecule whose ground and n-valence excited states can be described accurately by SR models (except for the doubly excited Z-state), it becomes a diradical at the barrier, when the Jt-bond is completely broken (13). Thus, at the twisted geometry all of ethylene s Jt-valence states (N, T, V, and Z) are two-configurational, except for the high-spin components of the triplet. 

Those arising from configurations that differ from the ground configuration by one 2s 2p transition. This may be called a valence excited configuration. The lines connecting these states are marked with a V . 

The ground state of the C atom is P from a 2s 2p configuration. In the case of B we saw that the excited valence configuration played an important role in the structures describing the B2 molecule. C2 has more electrons with the possibility of more bonds, and, thus, there may be more tendency for the valence excited configuration to be important in this molecule than in B2. 

The two P atoms could form two p bonds to produce a S+ ground state. If the valence excited state is important as argued above, these two states could also couple to S+ interacting strongly with the two pn bonds. 

We show the standard tableaux function results for the energy minimum geometry in Table 11.11. Here we see that the valence excited configuration has become the dominant stmcture, and the coupling of the P atomic ground states is structure 2. Structure 3 is a mixture of the and P states while stmcture 4 is another of tiie standard tableau associated with stmcture 1. 

From Table 11.3 we see that the ground state of 0 is P, and there are only two unpaired orbitals in the ground configuration. Since the L shell is more than half full, valence excitations will not reduce the number of double occupations. We can make the following conjectures. 

In Section 11.1 we pointed out that B and C atoms have relatively low-lying valence excited states compared to the other atoms considered. It is seen that these valence excited states comprise the principal stmctures in the bonded state of B2 and C2, but not in the other molecules where they contribute less than the ground configuration. We shall discuss these elfects in further detail for C atoms in Chapter 13. If we treat the one- and three-electron bonds as one-half a bond we see that B2, C2, N2,02, and F2 have two, three, three, two, and one bond(s) in the molecule, respectively. Were it not for the low-lying valence excited states in B and C, the molecules corresponding to these might be expected to have one and two bonds, respectively. Nevertheless, the more open stmcture of the valence excited states allows more bonding between the atoms. 

The low threshold energies for the production of D( S), 0( P), and 0( D2) show the importance of valence excited states in the BSD of neutral fragments [47]. The pathway for D( S) desorption probably involves D O D -I- OD. Ffowever, the thresholds for producing 0( P2) and 0( D2), which are the same within experimental error, are lower than the 9.5-and 11.5-eV thermodynamic energies required to produce 0( P2) + 2D( S) and 0( D2) + 2D( S), respectively. The low threshold values therefore indicate that the formation of 0( P2) and 0( D2) must occur by a pathway which involves simultaneous formation of D2. Kimmel et al. have in fact reported [46] a threshold for the production of D2 from D2O ice at — 6 to 7 eV, which supports this conclusion. Above the ionization threshold of amorphous ice, these excited states can be formed directly or via electron-ion recombination. 

Therefore, the energy separation between 5 i and Ti is 1 eV. For Rydberg-type excitations, the separation is, as a rule, 0.1 eV for valence-type excitations, it is 1-2 eV [22]. The separation of 1 eV is in favor of valence excitations in agreement with the results of those quenching experiments in which the kinetic distance was found to be comparable with the molecule diameter (Sec. 3.1). 

P. Strodel and P. Tavan. A revised MRCI-algorithm coupled to an effective valence-shell Hamiltonian. 11. Application to the valence excitations of butadiene, J. Chem. Phys., 117 4677 683 (2002). 

D. M. Neumark I would like to make a comment to Prof. Schlag. One expects an anion ZEKE spectrum to have the same overall intensity profile as the corresponding photoelectron spectrum only if direct detachment is the only process that occurs. However, FeO has several dipole-bound and valence-excited states near the detachment threshold. 

J. Oddershede, N. Elander, Spectroscopic Constants and Radiative Lifetimes for Valence-Excited Bound States, J. Chem. Phys. 56 (1972) 3495. 

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. 

This deficiency in the LDA/GGA has clear implications for the calculated excitation energies through the TDDFRT zero order (o = ea — e, of (10). For valence-type excitations, the above-mentioned LDA/GGA potential shift does not affect the 6)k° very strongly. This is because in this case the occupied (pi and virtual bulk region. Due to this, their LDA/GGA energies e, and ea will have similar upward shifts, which will cancel each other in the orbital energy difference (10). This explains the rather decent estimates of valence excitations which were obtained within TDDFRT with LDA/GGA. 

With this method, we clarified the electronic structures of the ground and excited states of benzene, butadiene, methane, and hydrogen molecules [1,2]. We also applied the method to valence excited states of polyenes [3] and then-cations [4]. In previous studies, we put our focus on the formalism of CASVB and its applicability to molecules in their equilibrium structures. 

Docken and Hinze108 have presented a very detailed study of the potential-energy curves for five valence excited states of LiH by the MCSCF method. In this type of calculation, the wavefunction, expressed in the form (5), is variationally optimized... 

D. Non-metal Oxides.—CO, SiO, and CS. The literature on CO is very extensive, and much early work is discussed in ref. 1, together with an analysis of recent extensive calculations on the valence excited states. O Neil and Schaefer313 carried out minimal-basis full Cl calculations on 72 states of CO at nine values of R. Seventeen bound states were predicted, eight of which have been observed experimentally, and the ordering is in agreement with experiment except for the a8II and A n states. Very detailed information is available in this investigation. 

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