Planar molecule

The Hamiltonian provides a suitable analytic form that can be fitted to the adiabatic surfaces obtained from quantum chemical calculations. As a simple example we take the butatriene molecule. In its neutral ground state it is a planar molecule with D2/1 symmetry. The lowest two states of the radical cation, responsible for the first two bands in the photoelectron spectrum, are and... 

We now consider planar molecules. The electronic wave function is expressed with respect to molecule-fixed axes, which we can take to be the abc principal axes of ineitia, namely, by taking the coordinates (x,y,z) in Figure 1 coincided with the principal axes a,b,c). In order to detemiine the parity of the molecule through inversions in SF, we first rotate all the electrons and nuclei by 180° about the c axis (which is peipendicular to the molecular plane) and then reflect all the electrons in the molecular ab plane. The net effect is the inversion of all particles in SF. The first step has no effect on both the electronic and nuclear molecule-fixed coordinates, and has no effect on the electronic wave functions. The second step is a reflection of electronic spatial coordinates in the molecular plane. Note that such a plane is a symmetry plane and the eigenvalues of the corresponding operator then detemiine the parity of the electronic wave function. 

We now consider planar molecules. The electronic wave function is expressed with respect to molecule-fixed axes, which we can take to be the abc principal axes of inertia, namely, by taking the coordinates (x,y,z) in Figure 1 coincided with the principal axes (a, b, c). In order to determine the parity of the molecule through inversions in SF, we first rotate all the displacement vectors... 

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]. 

Boron trifluoride is a trigonal planar molecule There are six electrons two for each B—F bond associated with the valence shell of boron These three bonded pairs are farthest apart when they are coplanar with F—B—F bond angles of 120°... 

Multiple bonds are treated as a single unit m the VSEPR model Formaldehyde is a trigonal planar molecule m which the electrons of the double bond and those of the two single bonds are maximally separated A linear arrangement of atoms m carbon diox ide allows the electrons m one double bond to be as far away as possible from the elec Irons m the other double bond... 

FIGURE 18 6 Acrolein w (H2C=CHCH=0) is a planar molecule Oxygen and each carbon IS sp hybridized and each contributes one elec tron to a conjugated tt elec tron system analogous to that of 1 3 butadiene... 

A second common example of the utility of INDO over CNDO is the methyl radical CH3. This planar molecule is a free radical with... 

If a molecule has a plane of symmetry, for which the symbol is a, reflection of all the nuclei through the plane to an equal distance on the opposite side produces a configuration indistinguishable from the initial one. Figure 4.3(a) shows the two planes of symmetry, (7 (xz) and (yfyz), of H2O using conventional axis notation. Just as theyz plane, the plane of the molecule, is a plane of symmetry so any planar molecule has at least one plane of symmetry. The subscript u stands for vertical and implies that the plane is vertical with respect to the highest-fold axis, C2 in this case, which defines the vertical direction. 

In the planar molecule BF3, in Figure 4.3(b), the C3 axis through B and perpendicular to the figure is the highest-fold axis and, therefore, the three planes of symmetry, perpendicular to the figure and through each of the B-F bonds, are labelled (t . The plane of the molecule is also a plane of symmetry and is labelled u , where /z stands for horizontal with respect to C3. 

As in diatomic molecules the structure of greatest importance is the equilibrium structure, but one rotational constant can give, at most, only one structural parameter. In a non-linear but planar molecule the out-of-plane principal moment of inertia 4 is related to the other two by... 

T( p") in Equation (7.126) and the product x T( p") is totally symmetric (or contains the totally symmetric species). There may be several Au, = 0 sequences in various vibrations i but only those vibrations with levels of a sufficiently low wavenumber to be appreciably populated (see Equation 7.83) will form sequences. In a planar molecule the lowest wavenumber vibrations are usually out-of-plane vibrations. 

Boron tnhahdes, BX, are trigonal planar molecules which are sp hybridized. The X—B—X angles are 120°. Important physical and thermochemical data are presented in Table 1 (8—14). Additional thermodynamic and spectroscopic data may be found in the hterature (1 5). 

Discernible associative character is operative for divalent 3t5 ions through manganese and the trivalent ions through iron, as is evident from the volumes of activation in Table 4. However, deprotonation of a water molecule enhances the reaction rates by utilising a conjugate base 7T- donation dissociative pathway. As can be seen from Table 4, there is a change in sign of the volume of activation AH. Four-coordinate square-planar molecules also show associative behavior in their reactions. 

Structure. Ethylene is a planar molecule with a carbon—carbon bond distance of 0.134 nm, which is shorter than the C—C bond length of 0.153 nm found in ethane. The C—H bond distance is 0.110 nm, and the bond angles are [Pg.432]

The basic pteridine nucleus (1) consists, according to X-ray crystallographic studies (75JCS(P2)40), of a more or less planar molecule with no unexpected features in so far as... 

Mi ellaneous Characterizing Constants The radius of gyration (R) is a simultaneous size-shape fac tor varying with the manner in which mass is distributed about the center of gravity of the molecule. For planar molecules, the radius of gyration is... 

While HiickeTs 4n + 2 rule applies only to monocyclic systems, HMO flieory is applicable to many other systems. HMO calculations of fused-ring systems are carried out in much the same way as for monocyclic species and provide energy levels and atomic coefficients for the systems. The incorporation of heteroatoms is also possible. Because of the underlying assumption of orthogonality of the a and n systems of electrons, HMO dieory is restricted to planar molecules. 

The process of constructing the MOs of ethylene is similar to that used for carbon monoxide, but the total number of AOs is greater, 12 instead of 8, because of the additional AOs from hydrogen. We must first define the symmetry of ethylene. Ethylene is known from experiment to be a planar molecule. 

One important structural feature on which to focus is whether the nitrogen atom lies in the same plane as the three carbon atoms. Electron diffraction experiments have found the ground state to be slightly non-planar. You can determine the planarity of the structures you compute by examining the sum of the three C-N-C angles (for a planar molecule, the sum will be 360°) and by looking at the values of the C2-N-C4-O and C3-N-C4 Hg dihedral angles (in a planar structure, both will be 0°). 

Carbon oxohalides are reactive gases or volatile liquids which feature planar molecules of C2t, symmetry they are isoelectronic with BX3 (p. 196) and the bonding is best described in terms of molecular orbitals spanning all 4 atoms rather than in terms of localized orbitals as... 

Nitryl fluoride and chloride, XNO2, like their nitrosyl analogues, are reactive gases they feature planar molecules, analogous to the... 

Figure 17.7 Molecular structures of (a) CIF3 and (b) BrFa as determined by microwave spectroscopy. An X-ray study of crystalline CIF3 gave slightly longer distances (171.6 and 162.1 pm) and a slightly smaller angle (87.0 "). (c) Structure of laCl showing planar molecules of approximate Da symmetry.

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