Modelling Molecules Electronic States

Photon absorption produces excited electron configurations by promotion of an electron from an occupied to a vacant MO. These electronic transitions are described as  

Neglecting the filled low-energy o-orbitals, the electronic configuration of the lowest electronic state (the ground state) is tt2n2. Photon absorption of the appropriate energy results in excited-state configurations by promotion of one electron from an occupied molecular orbital 

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It should be noted that nuclei and electrons are treated equivalently in //, which is clearly inconsistent with the way that we tend to think about them. Our understanding of chemical processes is strongly rooted in the concept of a potential energy surface which determines the forces that act upon the nuclei. The potential energy surface governs all behaviour associated with nuclear motion, such as vibrational frequencies, mean and equilibrium intemuclear separations and preferences for specific conformations in molecules as complex as proteins and nucleic acids. In addition, the potential energy surface provides the transition state and activation energy concepts that are at the heart of the theory of chemical reactions. Electronic motion, however, is never discussed in these terms. All of the important and useful ideas discussed above derive from the Bom-Oppenheimer approximation, which is discussed in some detail in section B3.1. Within this model, the electronic states are solutions to the equation... 

The corresponding fiinctions i-, Xj etc. then define what are known as the normal coordinates of vibration, and the Hamiltonian can be written in tenns of these in precisely the fonn given by equation (AT 1.69). witli the caveat that each tenn refers not to the coordinates of a single particle, but rather to independent coordinates that involve the collective motion of many particles. An additional distinction is that treatment of the vibrational problem does not involve the complications of antisymmetry associated with identical fennions and the Pauli exclusion prmciple. Products of the nonnal coordinate fiinctions neveitlieless describe all vibrational states of the molecule (both ground and excited) in very much the same way that the product states of single-electron fiinctions describe the electronic states, although it must be emphasized that one model is based on independent motion and the other on collective motion, which are qualitatively very different. Neither model faithfully represents reality, but each serves as an extremely usefiil conceptual model and a basis for more accurate calculations. 

In Section IV.A.4, we show what this general model looks like in the case of H electronic states of symmehic tetraatomic molecules. The situation in H states of asymmetric tetraatomics is briefly discussed in Section IV.B, where we present the handling of a concrete case, the X Uu state of the HCCS radical. For A states the reader is referred to original references [18,149,150,153]. 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

At a physical level. Equation 35 represents a mixing of all of the possible electronic states of the molecule, all of which have some probability of being attained according to the laws of quantum mechanics. Full Cl is the most complete non-relativistic treatment of the molecular system possible, within the limitations imposed by the chosen basis set. It represents the possible quantum states of the system while modelling the electron density in accordance with the definition (and constraints) of the basis set in use. For this reason, it appears in the rightmost column of the following methods chart ... 

The treatment developed here is based on the density matrix of quantum mechanics and extends previous work using wavefunctions.(42 5) The density matrix approach treats all energetically accessible electronic states in the same fashion, and naturally leads to average effective potentials which have been shown to give accurate results for electronically diabatic collisions. 19) The approach is taken here for systems where the dynamics can be described by a Hamiltonian operator, as it is possible for isolated molecules or in models where environmental effects can be represented by terms in an effective Hamiltonian. 

II electronic states, 634-640 theoretical background, 625-626 triatomic molecules, 611-615 pragmatic models, 620-621 Ab initio multiple spawning (AIMS) conical intersection location, 491-492 direct molecular dynamics, 411-414 theoretical background, 360-361 Adiabatic approximation geometric phase theory ... 

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