Polyatoms, defined

The first study in which a full CASSCE treatment was used for the non-adiabatic dynamics of a polyatomic system was a study on a model of the retinal chromophore [86]. The cis-trans photoisomerization of retinal is the primary event in vision, but despite much study the mechanism for this process is still unclear. The minimal model for retinal is l-cis-CjH NHj, which had been studied in an earlier quantum chemisti7 study [230]. There, it had been established that a conical intersection exists between the Si and So states with the cis-trans defining torsion angle at approximately a = 80° (cis is at 0°). Two... 

There may he as many basis sets defined for polyatomic calculations as there are cpiantum chemists One would like to define, m advance, the standard basis sets that will he suitable to most users. However, one also wants to allow sophisticated users the capability to modify existing basis sets or define their own basis sets. We have thus defined a IlyperChem basis set file format and included with IlyperChem a number of these. BAS files that define standard basis sets. Users, however, can define as many of their own basis sets as they like using Ih is file formal. The details of th e IlyperChem basis set file formal are described in the IJypcrChcm iie.fe.rm ce m anital. 

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

The vibrational temperature, defined for a diatomic harmonic oscillator by the temperature in Equation (5.22), is considerably higher because of the low efficiency of vibrational cooling. A vibrational temperature of about 100 K is typical although, in a polyatomic molecule, it depends very much on the nature of the vibration. 

It is now fundamental to define the normal coordinates of this vihrational system - that is to say, the nuclear displacements in a polyatomic molecule. Again in the limit of small amplitudes of vibration, the normal coordinates in the form of the vector Q, are related to the internal coordinates by a linear transformation, viz. 

Mulliken introduced the term "orbital" distinct from "orbital wave function" in 1932 in the second of fourteen papers carrying the general title, "Electronic Structures of Polyatomic Molecules and Valence." Mulliken defined atomic orbitals (AOs) and molecular orbitals (MOs) as something like the... 

When treating polyatomics it is convenient to define an average molecular partition function, In = (lnQ)/N, for an assembly of N molecules. In the dilute vapor (ideal gas) this introduces no difficulty. There is no intermolecular interaction and In = (In Q)/N = ln(q) exactly (q is the microcanonical partition function). In the condensed phase, however, the Q s are no longer strictly factorable. Be that as it may, continuing, and assuming In = (In Q)/N, we are led to an approximate result which is superficially the same as Equation 5.10,... 

As was mentioned in the preceding section, the infra-red stretching vibration bands of chalcogenoanions appear usually as more or less smeared-out bands. In contrcist, the infra-red spectra of small amounts of polyatomic anions isolated in eilkah halide host lattices have very sharp bands [see results in Refs. 204—209)]. Thus, one can clearly see that the bands are better defined when the anion can be effectively isolated and thereby ehminate the coupling between neighboring identical ions as well as reducing the other effects discussed earlier. More will be said about this in the next section. 

The concept of a reaction co-ordinate in organic chemistry is one that is not simply defined, since for a polyatomic system of n atoms it may depend on as many as 3n — 6 parameters for complete characterization. The reaction co-ordinate used by organic chemists in their representation of a reaction profile has only a qualitative significance. For example, that for an SN2 process on a methyl derivative is generally equated with the change in either the... 

By means of mass spectrometry, the mass of atoms and molecules, via mass-separated charged atomic or polyatomic ions, can be determined by measuring the mass-to-charge ratio m/z), whereby the mass of an atom or a molecule is not measured in g or kg, but in a multiple of the atomic mass constant mu (atomic mass unit). The atomic mass unit mu is defined as one-twelfth the mass of a neutral 12C atom, ma (12C), in its ground state ... 

Molecular rotation In a normal crystal every atom occupies a precise mean position, about which it vibrates to a degree depending on the temperature molecules or polyatomic ions have precisely defined orientations as well as precise mean positions. When such a crystal is heated, the amplitude of the thermal vibrations of the atoms increases with the temperature until a point is reached at which the regular structure breaks down, that is, the crystal melts. But in a few types of crystal it appears that notation of molecules or polyatomic... 

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