Molecule, linear

Cyanogen chloride, CICN. Colourless liquid, m.p. — C,b.p. 13 C(aqueousCN plusCl2). Linear molecule, polymerizes to cyanuric chloride (CICN),. Extremely poisonous. 

Dinitrogen oxide, nitrous oxide, N2O. Colourless gas, m.p. —9T C, b.p. —88-5°C (heat on NH4NO3). Decomposes to N2 and O2 above SOO C can be detonated. Linear molecule NNO. Used as a mild anaesthetic. 

Rigid linear molecules are a special case in which an extended MS group, rather than the MS group, is isomorphic to the point group of the equilibrium structure see chapter 17 of [1]. 

For interactions between two quadmpolar molecules which have 0 and 0g of the opposite sign, at a fixed separation r, the angular factor in equation (A1.5.13t leads to a linear stmcture, 0 = 0g = 0, being the most attractive. Linear molecules may also prefer a 2 rectangular or non-planar cross arrangement with 0 = 0g = nil, which allows them to approach closer and increase the radial factor. 

The electronic selection mles for linear molecules are as follows. AA = 0, + 1. A5 = 0. Again, these are really... 

The simplest case is a transition in a linear molecule. In this case there is no orbital or spin angular momentum. The total angular momentum, represented by tire quantum number J, is entirely rotational angular momentum. The rotational energy levels of each state approximately fit a simple fomuila ... 

The electrostatic interaction results from the interaction of tire ion with the pennanent multipole moments of the neutral. For cylindrically synnnetric neutrals or linear molecules, the ion-neutral multipole interaction is... 

For both types of orbitals, the coordinates r, 0 and cji refer to the position of the electron relative to a set of axes attached to the centre on which the basis orbital is located. Although STOs have the proper cusp behaviour near the nuclei, they are used primarily for atomic- and linear-molecule calculations because the multi-centre integrals which arise in polyatomic-molecule calculations caimot efficiently be perfonned when STOs are employed. In contrast, such integrals can routinely be done when GTOs are used. This fiindamental advantage of GTOs has led to the dominance of these fimetions in molecular quantum chemistry. 

For chemically bound molecules, it is usual to analyse tlie vibrational energy levels in teniis of normal modes, a non-linear (or linear) molecule witli V atoms has 3 V - 6 (or 3 V - 5) vibrational degrees of freedom. There is a... 

Polymers without configurational regularity are called atactic. Configurationally regular polymers can fonn crystalline stmctures, while atactic polymers are almost always amorjihous. Many polymers consist of linear molecules, however, nonlinear chain architectures are also important (figure C2.1.2). 

Vibronic Coupling in Singlet States of Linear Molecules... 

Until now we have implicitly assumed that our problem is formulated in a space-fixed coordinate system. However, electronic wave functions are naturally expressed in the system bound to the molecule otherwise they generally also depend on the rotational coordinate 4>. (This is not the case for E electronic states, for which the wave functions are invariant with respect to (j> ) The eigenfunctions of the electronic Hamiltonian, v / and v , computed in the framework of the BO approximation ( adiabatic electronic wave functions) for two electronic states into which a spatially degenerate state of linear molecule splits upon bending. 

The expressions for the rotational energy levels (i.e., also involving the end-over-end rotations, not considered in the previous works) of linear triatomic molecules in doublet and triplet II electronic states that take into account a spin orbit interaction and a vibronic coupling were derived in two milestone studies by Hougen [72,32]. In them, the isomorfic Hamiltonian was inboduced, which has later been widely used in treating linear molecules (see, e.g., [55]). 

The aqueous solution has a low conductivity, indicating that mercury(II) chloride dissolves essentially as molecules Cl—Hg—Cl and these linear molecules are found in the solid and vapour. A solution of mercury(II) chloride is readily reduced, for example by tin(ll) chloride, to give first white insoluble mercury(I) chloride and then a black metallic deposit of mercury, The complexes formed from mercury(II) chloride are considered below. 

For the model Hamiltonian used in this study it was assumed that bond stretching satisfactorily describes all internal vibrational motions for a system of linear molecules and the split parts of the Hamiltonian were of the form... 

SISM for an Isolated Linear Molecule An efficient symplectic algorithm of second order for an isolated molecule was studied in details in ref. [6]. Assuming that bond stretching satisfactorily describes all vibrational motions for linear molecule, the partitioned parts of the Hamiltonian are... 

We shall illustrate the SISM described with two examples. The model system of a box of water molecules and the system of a box of linear molecules which are depicted in Figure 2. 

Isolated Linear Molecule Figure 6 shows the error in total energy for an isolated linear molecule H-(-C=C-)5-H. It is obvious that for the same level of accuracy, the time step in the SISM can be ten times or more larger as in the LFV. Furthermore, the LFV method is stable for only very short time steps, up to 5 fs, while the SISM is stable even for a time step up to 200 fs. However, such large time steps no longer represent physical reality and arc a particular property identified with linear molecules without bending or torsional intramolecular interactions. 

These equations reduce to a 3 x 3 matrix Ricatti equation in this case. In the appendix of [20], the efficient iterative solution of this nonlinear system is considered, as is the specialization of the method for linear and planar molecules. In the special case of linear molecules, the SHAKE-based method reduces to a scheme previously suggested by Fincham[14]. 

An N-atom molecular system may he described by dX Cartesian coordinates. Six independent coordinates (five for linear molecules, three fora single atom) describe translation and rotation of the system as a whole. The remaining coordinates describe the nioleciiUir configuration and the internal structure. Whether you use molecular mechanics, quantum mechanics, or a specific computational method (AMBER, CXDO. etc.), yon can ask for the energy of the system at a specified configuration. This is called a single poin t calculation. ... 

---