Semiempirical molecules

Jones et al. [144,214] used direct dynamics with semiempirical electronic wave functions to study electron transfer in cyclic polyene radical cations. Semiempirical methods have the advantage that they are cheap, and so a number of trajectories can be run for up to 50 atoms. Accuracy is of course sacrificed in comparison to CASSCF techniques, but for many organic molecules semiempirical methods are known to perform adequately. 

SEMIEMPIRICAL CALCULATIONS ON LARGER MOLECULES The spin eigenfunctions are orthogonal... 

Having the Slater atomic orbitals, the linear combination approximation to molecular orbitals, and the SCF method as applied to the Fock matrix, we are in a position to calculate properties of atoms and molecules ab initio, at the Hartree-Fock level of accuracy. Before doing that, however, we shall continue in the spirit of semiempirical calculations by postponing the ab initio method to Chapter 10 and invoking a rather sophisticated set of approximations and empirical substitutions... 

In formulating a mathematical representation of molecules, it is necessary to define a reference system that is defined as having zero energy. This zero of energy is different from one approximation to the next. For ah initio or density functional theory (DFT) methods, which model all the electrons in a system, zero energy corresponds to having all nuclei and electrons at an infinite distance from one another. Most semiempirical methods use a valence energy that cor-... 

Semiempirical calculations have been very successful in the description of organic chemistry, where there are only a few elements used extensively and the molecules are of moderate size. Some semiempirical methods have been devised specifically for the description of inorganic chemistry as well. The following are some of the most commonly used semiempirical methods. 

The most severe limitation of ah initio methods is the limited size of the molecule that can be modeled on even the largest computers. Semiempirical calculations can be used for large organic molecules, but are also too computation-intensive for most biomolecular systems. If a molecule is so big that a semiempirical treatment cannot be used elfectively, it is still possible to model its behavior avoiding quantum mechanics totally by using molecular mechanics. 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

It is possible to use computational techniques to gain insight into the vibrational motion of molecules. There are a number of computational methods available that have varying degrees of accuracy. These methods can be powerful tools if the user is aware of their strengths and weaknesses. The user is advised to use ah initio or DFT calculations with an appropriate scale factor if at all possible. Anharmonic corrections should be considered only if very-high-accuracy results are necessary. Semiempirical and molecular mechanics methods should be tried cautiously when the molecular system prevents using the other methods mentioned. 

QSPR methods have yielded the most accurate results. Most often, they use large expansions of parameters obtainable from semiempirical calculations along with other less computationally intensive properties. This is often the method of choice for small molecules. 

For ah initio, semiempirical, or molecular dynamics calculations, the amount of CPU time necessary is generally the factor of greatest concern to researchers. For very large molecules, memory use is of concern for molecular mechanics... 

Semiempiricals n - For small- to medium-size molecules (limited by integrals)... 

Semiempiricals For very large molecules (limited by matrix inversion)... 

Both molecular dynamics studies and femtosecond laser spectroscopy results show that molecules with a sufficient amount of energy to react often vibrate until the nuclei follow a path that leads to the reaction coordinate. Dynamical calculations, called trajectory calculations, are an application of the molecular dynamics method that can be performed at semiempirical or ah initio levels of theory. See Chapter 19 for further details. 

The most commonly used semiempirical for describing PES s is the diatomics-in-molecules (DIM) method. This method uses a Hamiltonian with parameters for describing atomic and diatomic fragments within a molecule. The functional form, which is covered in detail by Tully, allows it to be parameterized from either ah initio calculations or spectroscopic results. The parameters must be fitted carefully in order for the method to give a reasonable description of the entire PES. Most cases where DIM yielded completely unreasonable results can be attributed to a poor fitting of parameters. Other semiempirical methods for describing the PES, which are discussed in the reviews below, are LEPS, hyperbolic map functions, the method of Agmon and Levine, and the mole-cules-in-molecules (MIM) method. 

The simplest and most quickly computed models are those based solely on steric hindrance. Unfortunately, these are often too inaccurate to be trusted. Molecular mechanics methods are often the method of choice due to the large amount of computation time necessary. Semiempirical methods are sometimes used when molecular mechanics does not properly represent the molecule. Ah initio methods are only viable for the very smallest molecules. These are discussed in more detail in the applicable chapters and the sources mentioned in the bibliography. 

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

There is one semiempirical program, called HyperNMR, that computes NMR chemical shifts. This program goes one step further than other semiempiricals by defining different parameters for the various hybridizations, such as sp carbon vs. sp carbon. This method is called the typed neglect of differential overlap method (TNDO/1 and TNDO/2). As with any semiempirical method, the results are better for species with functional groups similar to those in the set of molecules used to parameterize the method. 

Another semiempirical method, incorporated in the VAMP program, combines a semiempirical calculation with a neural network for predicting the chemical shifts. Semiempirical calculations are useful for large molecules, but are not generally as accurate as ah initio calculations. 

For large molecules, the choice between semiempirical calculations and empirical calculations should be based on a test case. 

Organic molecules are generally composed of covalent bonded atoms with several well-defined hybridization states tending to have well-understood preferred geometries. This makes them an ideal case for molecular mechanics parameterization. Likewise, organic molecules are the ideal case for semiempirical parameterization. 

Molecular mechanics force fields are sometimes parameterized to describe lanthanides and actinides. This has been effective in describing the shape of the molecule, but does not go very far toward giving systematic energies. A few semiempirical methods have been parameterized for these elements, but they have not seen widespread use. 

---