Reference bond angle

The coefficients C are chosen to ensure that the function has a minimum at the appropriate reference bond angle. For linear, trigonal, square planar and octahedral coordination, Fourier series with just two terms are used with a Cq term and a term for n = 1, 2, 3 or 4, respectively ... 

Carbene analog max(nm) Reference Bond angle (deg) (method3) Reference... 

This equation was derived previously for the case of 1,2 dichloroethylene (equation 2.17). The possible permutations for neighboring bonds with a threefold potential barrier can be represented by a statistical weight matrix composed of elements based on individual statistical weights. The matrix methods involved are described in Appendix 2E. The reference bond angle Q, is placed in a right-handed coordinate system. Transformation matrices A[ (see for example equation 2C.25) are then used to transform the coordinates of the Ql bond into that of the (2, one. The process is repeated until the coordinates of all the bonds in a given conformation are generated. 

The simplest description of the energy required to deform a bond angle (0) from the reference bond angle (6°) is the quadratic, Hooke s law type expression in equation (5),... 

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

As for bond stretching, the simplest description of the energy necessary for a bond angle to deviate firom the reference value is a harmonic potential following Hooke s law, as shown in Eq. (22). 

Any length, bond angle, or torsion defined in a named selection (see the lype.Kfhe.m Reference Manual)... 

If we assume that there are certain "ideal" values for bond angles, bond distances, and so on, it follows that deviations from these ideal values will destabilize a particular structure and increase its potential energy. This increase in potential energy is referred to as the strain energy of the structure. Other terms for this increase include steric energy and steric strain. Arithmetically, the total strain energy (fj of an alkane or cycloalkane can be considered as... 

Strong sp -sp a bonds are not possible for cyclopropane, because the 60° bond angles of the ring do not permit the orbitals to be properly aligned for effective overlap (Figure 3.10). The less effective overlap that does occur leads to what chemists refer to as bent bonds. The electron density in the carbon-carbon bonds of cyclopropane does not lie along the internuclear- axis but is distr-ibuted along an arc between the two carbon atoms. The r-ing bonds of cyclopropane are weaker than other carbon-carbon a bonds. 

Sources for bond lengths, bond angles, and dihedral angles include the published literature, standard references like the CRC series, and previous calculations. Z-matrices may also be created by the NewZMat utility from data generated by a wide variety of drawing packages. Refer to the Quick Start for a sample conversion operation for your version of Gaussian. 

We refer to models where we write the total potential energy in terms of chemical endties such as bond lengths, bond angles, dihedral angles and so on as valence force field models. 

Reference to the Walsh diagram (Figure 2.105) shows that for a MNO 8 system, bending produces a net stabilization, thus rationalizing the M—N—O bond angle of c. 120° found for systems like M(NO)Cl2(PR3)2. 

Sulfone molecular structures, including sulfuryl halides, have been repeatedly reviewed through the late seventies28 and early eighties5. Scheme 1 contains a list of the compounds discussed in these references. While the structures of these compounds will be discussed, recent structural information that was not included in the above compilations will be described initially. The relevant substances are listed in Table 3 along with the S=0 bond lengths and OSO bond angles. 

FIGURE 21. Sulfur bond angles in analogous sulfones, sulfoxides and sulfides with various ligands (cf. Reference 5). 

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