In large molecules

Experimental access to the probabilities P(E ,E) for energy transfer in large molecules usually involves teclmiques providing just the first moment of this distribution, i.e. the average energy (AE) transferred in a collision. Such methods include UV absorption, infrared fluorescence and related spectroscopic teclmiques [11. 28. 71. 72, 73 and 74]. More advanced teclmiques, such as kinetically controlled selective ionization (KCSI [74]) have also provided infonnation on higher moments of P(E ,E), such as ((AE) ). 

Brito Cruz C H, Fork R L, Knox W H and Shank C V 1986 Spectral hole burning in large molecules probed with 10 fs optical pulses Chem. Phys. Lett. 132 341-5... 

Bardeen C J and Shank C V 1993 Femtosecond electronic dephasIng In large molecules In solution using mode suppression Chem. Phys. Lett. 203 535-9... 

Farkas O and Schlegel H B 1998 Methods for geometry optimization In large molecules. I. An O(N ) algorithm for solving systems of linear equations for the transformation of coordinates and forces J. Chem. Phys. 109 7100... 

Elber R and Karplus M 1987 A method for determining reaction paths in large molecules application to myoglobin Chem. Phys. Lett. 139 375... 

The method presented in this chapter is aimed mainly at providing information on the presence of conical intersections in large molecules, and helps in the calculation of their energies and structures. In this section, we review briefly some other procedures used to characterize conical intersections, and compare them with the present method. 

Elber R and M Karplus 1987. A Method for Determining Reaction Paths in Large Molecules Application to Myoglobin. Chemical Physics Letters 139 375-380. 

Molecular size smaller molecules move more quickly than larger ones as a result, C atoms in small molecules relax more slowly than those in large molecules. The C atoms in the more mobile cyclohexanes (T/ = 19-20 s) take longer than those in the more sluggish cyclodecane (f/ = 4 - 5 s)... 

For some compounds, it is especially useful to know the shape of the molecule. While this is critically important in large molecules made with a backbone of carbon, called organic molecules, it is often interesting in simpler molecules as well. The formula for water might cause you to think that a hydrogen atom was attached to another hydrogen atom, and then an oxygen atom was attached to them ... 

FIGURE 3.41 In large molecules, there are many closely spaced energy levels and the HOMO-LUMO gap is quite small. Such molecules are often colored because photons of visible light can be absorbed when electrons are excited from the HOMO to the LUMO. 

In large molecules that tumble slowly, the predominant relaxation pathway is via This is shown schematically in Fig. 4.2c. A part of the population x is now transferred from the /3q state to the a)3 state. This causes an increase in the population of the upper level of one 1 transition (/], level 3) and a decrease in the lower population level of the other I transition (4, level 2). As a result, the population difference between the lower and upper levels of each I transition is reduced to d — x (i.e., level 1 — level 3, or level 2 — level 4, becomes d — x). The reduction in population difference by x as compared to the equilibrium situation (Fig. 4.2a)... 

Assuming that a reasonable force field is known, the solution of the above equations to obtain the vibrational frequencies of water is not difficult However, in more complicated molecules it becomes very rapidly a formidable one. If there are N atoms in the molecule, there are 3N total degrees of freedom and 3N-6 for the vibrational frequencies. The molecular symmetry can often aid in simplifying the calculations, although in large molecules there may be no true symmetry. In some cases the notion of local symmetry can be introduced to simplify the calculation of vibrational frequencies and the corresponding forms of the normal modes of vibration. 

Yang ZZ, Wang CS (1997) Atom-bond electronegativity equalization method. 1. Calculation of the charge distribution in large molecules. J Phys Chem A 101(35) 6315-6321... 

Fischer, G. Spectroscopic Implications of Line Broadening in Large Molecules. 66,115-147 (1976). 

High-Throughput Quantitative Bioanalysis in Large Molecule DMPK.333... 

HIGH-THROUGHPUT QUANTITATIVE BIOANALYSIS IN LARGE MOLECULE DMPK... 

In large molecules, manual addition of all the SCS can be tedious and a computer programme was soon developed in order to do this automatically and others followed. ... 

Application, of the pulse method to measurements of short-lived singlet states in large molecules will be discussed in Section III.5). 

Figure 2. Explicitly correlated basis functions of the form rj2p (l) (2) that should be avoided in large molecules.

A Priori Elimination of Configurational Deadwood from Full Valence Spaces in Large Molecules... 

N. H. March, Differential-equation for the electron-density in large molecules. Int. J. Quantum Chem. 13, 3-8 (1986). 

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