Molecular electronic states

Martinez T J, BenNun M and Levine R D 1996 Multi-electronic-state molecular dynamics—a wavefunction approach with applications J. Phys. Chem. 100 7884... 

Electronic-State Molecular-Dynamics—A Wave-Function Approach with Applications. 

M. Amarouche, F. X. Gadea,and J. Durup, Chem. Phys., 130,145 (1989). A Proposal for the Theoretical Treatment of Multi-Electronic-State Molecular-Dynamics—Hemiquantal Dynamics with the Whole DIM Basis (HWD)—A Test on the Evolution of Excited Ar3 Cluster Ions. 

Molecular nitrogen, N2, is one of the most extensively studied diatomic molecules and optical spectroscopy has provided a wealth of information about its ground and excited electronic states. Molecular beam magnetic resonance studies of N2 in its ground state have yielded information about 14N nuclear spin dipolar and quadrupole interactions. Similar studies of N2 in its electronically excited A 3LU state were described in two very extensive papers by Freund, Miller, De Santis and Lurio [43] (paper I) and De Santis, Lurio, Miller and Freund [44] (paper II). We will describe their results and analysis in detail, but first note in passing that, strictly speaking, the lowest excited triplet state should be labelled the a state the label A has been used by all concerned in the past, so we will continue to do so. 

To illustrate the above concepts, we consider a two-electronic-state molecular model system, corresponding to keeping just two terms in the sum on the right-hand side (rhs) of Eq. (5), so thaf ( R, f) in Eq. (11) is a fwo-dimensional column vecfor and W( Ra) t), a (2 x 2) mafrix. A represenfafive of fhis class of models is fhe one-electron diatomic HJ molecule described in a two-electronic-state approximation. 

Nakamura and Truhlar [26] have developed direct calculation techniques to obtain quasi-diabatic states. Yet, a main issue remains there is no clear quantum-mechanical interpretation as to the meaning of an electronic wave ftinction that depends parametrically on the positive charge positions [4]. The multi-electronic-state molecular dynamics approach by Martinez et al. [27] highlights the problems raised by the use of the BO scheme. The crossing points and the uncontrolled coupling of electronic states... 

Electronic State Molecular Constants Reference fethod... 

Amarouche M, Gadea F, Dump J (1989) A proposal for the theoretical treatment of multi-electronic-state molecular dynamics hemiquantal dynamics with the whole dim basis (HWD). A test on the evolution of excited ar3- - cluster ions. Chem Phys 130 145-157... 

Martinez TJ, Ben-Nun M, Levine RD (1996) Multi-electronic-state molecular dynamics a wave function approach with applications. J Phys Chem 100 7884... 

Since solids do not exist as truly infinite systems, there are issues related to their temiination (i.e. surfaces). However, in most cases, the existence of a surface does not strongly affect the properties of the crystal as a whole. The number of atoms in the interior of a cluster scale as the cube of the size of the specimen while the number of surface atoms scale as the square of the size of the specimen. For a sample of macroscopic size, the number of interior atoms vastly exceeds the number of atoms at the surface. On the other hand, there are interesting properties of the surface of condensed matter systems that have no analogue in atomic or molecular systems. For example, electronic states can exist that trap electrons at the interface between a solid and the vacuum [1]. 

Much of the previous section dealt with two-level systems. Real molecules, however, are not two-level systems for many purposes there are only two electronic states that participate, but each of these electronic states has many states corresponding to different quantum levels for vibration and rotation. A coherent femtosecond pulse has a bandwidth which may span many vibrational levels when the pulse impinges on the molecule it excites a coherent superposition of all tliese vibrational states—a vibrational wavepacket. In this section we deal with excitation by one or two femtosecond optical pulses, as well as continuous wave excitation in section A 1.6.4 we will use the concepts developed here to understand nonlinear molecular electronic spectroscopy. 

Schinke R and Huber J R 1995 Molecular dynamics in excited electronic states—time-dependent wave packet studies Femtosecond Chemistry Proc. Berlin Conf. Femtosecond Chemistry (Berlin, March 1993) (Weinheim Verlag Chemie)... 

We now turn to electronic selection rules for syimnetrical nonlinear molecules. The procedure here is to examme the structure of a molecule to detennine what synnnetry operations exist which will leave the molecular framework in an equivalent configuration. Then one looks at the various possible point groups to see what group would consist of those particular operations. The character table for that group will then pennit one to classify electronic states by symmetry and to work out the selection rules. Character tables for all relevant groups can be found in many books on spectroscopy or group theory. Ftere we will only pick one very sunple point group called 2 and look at some simple examples to illustrate the method. 

Many of the fiindamental physical and chemical processes at surfaces and interfaces occur on extremely fast time scales. For example, atomic and molecular motions take place on time scales as short as 100 fs, while surface electronic states may have lifetimes as short as 10 fs. With the dramatic recent advances in laser tecluiology, however, such time scales have become increasingly accessible. Surface nonlinear optics provides an attractive approach to capture such events directly in the time domain. Some examples of application of the method include probing the dynamics of melting on the time scale of phonon vibrations [82], photoisomerization of molecules [88], molecular dynamics of adsorbates [89, 90], interfacial solvent dynamics [91], transient band-flattening in semiconductors [92] and laser-induced desorption [93]. A review article discussing such time-resolved studies in metals can be found in... 

In the ideal case for REMPI, the efficiency of ion production is proportional to the line strength factors for 2-photon excitation [M], since the ionization step can be taken to have a wavelength- and state-mdependent efficiency. In actual practice, fragment ions can be produced upon absorption of a fouitli photon, or the ionization efficiency can be reduced tinough predissociation of the electronically excited state. It is advisable to employ experimentally measured ionization efficiency line strengdi factors to calibrate the detection sensitivity. With sufficient knowledge of the excited molecular electronic states, it is possible to understand the state dependence of these intensity factors [65]. 

In its most fiindamental fonn, quantum molecular dynamics is associated with solving the Sclirodinger equation for molecular motion, whether using a single electronic surface (as in the Bom-Oppenlieimer approximation— section B3.4.2 or with the inclusion of multiple electronic states, which is important when discussing non-adiabatic effects, in which tire electronic state is changed [15,16, YL, 18 and 19]. 

The ultimate approach to simulate non-adiabatic effects is tln-ough the use of a fiill Scln-ddinger wavefunction for both the nuclei and the electrons, using the adiabatic-diabatic transfomiation methods discussed above. The whole machinery of approaches to solving the Scln-ddinger wavefiinction for adiabatic problems can be used, except that the size of the wavefiinction is now essentially doubled (for problems involving two-electronic states, to account for both states). The first application of these methods for molecular dynamical problems was for the charge-transfer system... 

A quantum mechanical treatment of molecular systems usually starts with the Bom-Oppenlieimer approximation, i.e., the separation of the electronic and nuclear degrees of freedom. This is a very good approximation for well separated electronic states. The expectation value of the total energy in this case is a fiinction of the nuclear coordinates and the parameters in the electronic wavefunction, e.g., orbital coefficients. The wavefiinction parameters are most often detennined by tire variation theorem the electronic energy is made stationary (in the most important ground-state case it is minimized) with respect to them. The... 

In quantum theory, physical systems move in vector spaces that are, unlike those in classical physics, essentially complex. This difference has had considerable impact on the status, interpretation, and mathematics of the theory. These aspects will be discussed in this chapter within the general context of simple molecular systems, while concentrating at the same time on instances in which the electronic states of the molecule are exactly or neatly degenerate. It is hoped... 

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