Electronic states of molecule

Just as it is possible to characterize the single-electron molecular orbitals using the relevant symmetry operations of the molecule, it is possible to characterize the total wave function using the same operations. The total wave function contains each and every electron coordinate. It is customary to characterize the single molecular orbitals by small letters and the total wave functions by capital letters. For example, we have the single orbital Og, and the total wave function Eg. 

For systems that contain only one electron there is no difference in the molecular-orbital and the total electronic wave function. For many-electron systems, however, there is a considerable difference. 

It should be noted that for many-electron systems it is only the symmetry of the total wave function which has physical (and chemical ) significance. This quantity is the only observable quantity.  

The ground state and the first and the second excited electronic 

The spin multiplicity, 2S + 1, where S is the value of the spin quantum number (here S = ), is the left-hand superscript. 

For systems that contain only one electron there is no difference in the molecular-orbital and the total electronic wave function. For many-electron systems, however, there is a considerable difference. It should be noted that for many-electron systems it is only the symmetry of the total wave function which has physical (and chemical ) significance. This quantity is the only observable quantity.  

Since the two orbitals are different, the two electrons can have the same spin. A total spin quantum number of one (S = 1) is obtained if both electrons have the same spin on the other hand, a spin quantum number of zero (S = 0) is obtained if the electrons have different spins. With the spin multiplicity equal to 2S + 1, we get both a triplet (S = 1) and a sii let (S = 0) state. 

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Simons J 1972 Energy-shift theory of low-lying excited electronic states of molecules J. Chem. Phys. 57 3787-92 A more recent overview of much of the EOM, Greens function, and propagator field is given in ... 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

Many chemical problems can be discussed by way of a knowledge of the electronic state of molecules. The electronic state of a molecular system becomes known if we solve the electronic Schrodinger equation, which can be separated from the time-independent, nonrelativistic Schrodinger equation for the whole molecule by the use of the Bom-Oppenheimer approximation D. In this approximation, the electrons are considered to move in the field of momentarily fixed nuclei. The nuclear configuration provides the parameters in the Schrodinger equation. 

On a somewhat higher level of qualitative MO argumentation, one can allow for the fact that the total energy of the molecule is not related only to the sum of energies of occupied orbitals, but also to certain electron repulsion terms. This leads to a better understanding of the nature of electronic states of molecules at biradicaloid geometries 19>U2> and, in particular, of the difference between Si and Ti hypersurfaces.19) We... 

All the above-mentioned experiments dealt with vibrational excitation of molecules by infrared laser lines. Inelastic collision processes in excited electronic states of molecules can be investigated in a similar way by means of visible or ultraviolet laserlines. 

Radiationless transitions among electronic states of molecules represent a class of relaxation processes that are electronic in nature. The general term electronic relaxation appears to be appropriate for these processes,23 but it is convenient to divide those transitions involving a change in the bound electronic states of a molecule into two categories Transitions between states of the same multiplicity, referred to as internal conversion, and transitions between states of different multiplicity, referred to as intersystem crossing. Although there are several early experimental... 

A phenomenon closely related to electronic relaxation is the existence of diffuseness in the absorption spectra of the higher excited electronic states of molecules. It has been known for some time that very fast electronic relaxation processes occur when the higher excited states of molecules are caused to interact with radiation. It is remarkable then that only in relatively recent work has the association between these fast processes and spectral diffuseness been clearly focused upon. These spectral results provide some of the most definitive features that may be associated with the electronic relaxation mechanisms. First, the results from solid-state spectra 62 ... 

We must realize, however, that such a description of a molecule involves drastic approximations thus only approximate numerical results can be obtained. It is possible by performing elaborate numerical calculations to obtain better and better approximations for the molecular wave functions. Here we shall be interested only in semiquantitative approximate schemes which allow us to place the low-lying electronic states of molecules. 

Ions formed by high energy radiation recombine eventually with electrons and when they do they may form excited electronic states of molecules and fragments of molecules. These states lose energy in various ways and cascade down to states which are formed by the more customary methods of photochemistry. Often the chemical effects of high energy radiation are not too different from those found in photochemistry. 

If relativistic effects are significant, the electronic states of molecules within the adiabatic approximation canbe obtained by solving the one-electron Dirac equation (Dirac, 1928,1958)... 

In recent years, the first applications of DFT to excited electronic states of molecules have been reported. In the so-called time-dependent DFT (TDDFT) method, the excitation energies are obtained as the poles of the frequency-dependent polarizability tensor [29], Several applications of TDDFT with standard exchange correlation functionals have shown that this method can provide a qualitatively correct description of the electronic excitation spectrum, although errors of the order of 0.5 eV have to be expected for the vertical excitation energies. TDDFT generally fails for electronic states with pronounced charge transfer character. 

Volume 13 G. Del Re, G. Berthier, J. Serre Electronic States of Molecules and Atom Ousters. Foundations and Prospects of Semiempirical Methods. 1980. VIII, 177 pages. 

Many free radicals in their electronic ground states, and also many excited electronic states of molecules with closed shell ground states, have electronic structures in which both electronic orbital and electronic spin angular momentum is present. The precession of electronic angular momentum, L, around the intemuclear axis in a diatomic molecule usually leads to defined components, A, along the axis, and states with A =0, 1, 2, 3, etc., are called , n, A, , etc., states. In most cases there is also spin angular momentum S, and the electronic state is then labelled 2,s+1 Id, 2,s+1 A, etc. 

Whereas density functional theory guaranties that for the ground electronic state of molecules the electron density determines the energy, the actual construction of such energy functions from first principles is a problem of considerable complexity. The electron densities computed by the MEDLA method suggest various approximations to the molecular energy of large systems. 

Name the electronic states of molecules with the uppercase roman letters A, B, E, and T the ground state is X. Use the corresponding lowercase letters for one-electron orbitals. A tilde ( ) is added for polyatomic molecules. The subscripts describe the symmetry of the orbital. 

The electronic states of molecules are also given empirical single letter labels as follows. The ground electronic state is labelled X, excited states of the same multiplicity are labelled A, B, C,.. . , in ascending order of energy, and excited states of different multiplicity are labelled with lower case letters a, b, c,.. . . In polyatomic molecules (but not diatomic molecules) it is customary to add a tilde (e.g. X) to these empirical labels to prevent possible confusion with the symmetry species label. 

These terms of electron configurations arising from different partially filled orbitals are very valuable in deciphering what excited electronic states of molecules and intermediates are possible and lie in an energy range accessible to the particular experiment. 

Fig. 3.15 Electronic states of molecules characterized by the orbitals involved and by the spin configuration of the electrons (spin multiplicity M = 2S-i-l, S=J]Sj and Sj= l/2, spin of individual electrons).

There are a number of different theoretical approaches to the calculation of the band structures of polymers. These are extensions of the methods employed to calculate the electronic states of molecules, which obtain molecular orbitals from a linear combination of atomic orbitals. In this case the states in question are those of an infinitely long molecule, which is approximated by a finite length system with cyclic boundary conditions, i.e. the right-hand end of the chain is, in effect, joined to the left-hand end of the chain. This is the method used for band... 

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