Semiempirical small molecules

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. 

Quantum mechanical and selected semiclassical and semiempirical methods for the calculation of electron impact ionization cross sections are described and their successes and limitations noted. Experimental methods for the measurement of absolute and relative ionization cross sections are also described in some detail. Four theoretical methods, one quantum mechanical and three semiclassical, have been used to calculate cross sections for the total ionization of the inert gases and small molecules and the results compared with experimental measurements reported in the literature. Two of the theoretical methods, one quantum mechanical and one semiclassical, have been applied to the calculation of orientation-dependent electron impact ionization cross sections and the results compared with recent experiments. 

The EM method has been tested on the inert gases and a range of small molecules and gives good agreement with experimental results in almost all cases.17 This method will be discussed further in relation to the orientation dependence of the electron impact ionization cross section in a later section. The semiempirical polarizability method described below was developed to calculate and to use it with the amax values obtained from this method in order to calculate the energy dependence of the cross section. 

The solvation models are used to predict the properties of small molecules and large biomolecules employing different levels of theory. In the prediction of solvent effect using electronic structure calculation, semiempirical, HF, post-HF, and DFT-based hybrid methods have been widely used [2-11], Since a wealth of literature is... 

Even though the G2 neutral test set is very valuable, it is biased towards small molecules and does not cover all bonding situations that may arise for a given element. The validation of semiempirical methods has traditionally been done using larger test sets which, however, have the drawback that the experimental reference data are often less accurate than those in the G2 set. 

In our own validation sets, experimental heats of formation are preferentially taken from recognized standard compilations [38-40]. If there are enough experimental data for a given element, we normally only use reference values that are accurate to 2 kcal/mol. If there is a lack of reliable data, we may accept experimental heats of formation with a quoted experimental error of up to 5 kcal/mol. This choice is motivated by the target accuracy of the established semiempirical methods. If experimental data are missing for a small molecule of interest, we consider it legitimate [18] to employ computed heats of formation from high-level ab initio methods as substitutes. 

However, most wave function based calculations also contain a semiempirical component. For example, the primitive Gaussian functions in all commonly used basis sets (e.g., the six Gaussian functions used to represent a li orbital on each first row atom in the 6-3IG basis set) are contracted into sums of Gaussians with fixed coefficients and each of these linear combinations of Gaussians is used to represent one of the independent basis functions that contribute to each AO. The sizes of the primitive Gaussians (compact versus diffuse) and the coefficient of each Gaussian in the contracted basis functions, are obtained by optimizing the basis set in calculations on free atoms or on small molecules." ... 

It has been said of semiempirical methods They will never outlive their usefulness for correlating properties across a series of molecules... I really doubt their predictive value for a one-off calculation on a small molecule on the grounds that whatever one is seeking to predict has probably already been included in with the parameters. (A. Hinchliffe, Ab Initio Determination of Molecular Properties , Adam Hilger, Bristol, 1987, p. x). Do you agree with this Why or why not Compare the above quotation with ref. [24], pp. 133-136. 

The statements above directly contradict the assertion that ...whatever one is seeking to predict has probably already been included in with the parameters. , with the reservation that Hinchcliffe was presumably writing about 5 years before Dewar. The references given by Dewar, and the experience of the many chemists who use semiempirical methods (not only the Dewar-type ones) show that these are not merely methods of interpolation . It is however true that for accurate, reliable information on the properties of a small molecule one would very likely resort to a high-level ab initio or DFT calculation. 

Most calculations on CPs have used semiempirical methods. The Hiickel method yields useful results and many properties can be qualitatively understood [188,190], but numbers are not quite reliable. The valence effective Hamiltonian (VEH) method [191] has been applied successfully to CPs [187,192]. It uses atomic potentials parametrized on the results of ab initio HF-SCF calculations on small molecules, and not on experimental data in that sense, it is a purely theoretical method. 

Since the early days of application of Mossbauer spectroscopy in solid state physics and inorganic chemistry, electronic structure calculations have been performed to rationalize and predict the Mossbauer parameters obtained. In the beginning, calculations were applied to single ions, but later semiempirical methods could be applied to small molecules, too. Early density functional theory (DFT) methods, like the self-consistent charge (SCC)-Xa method could be successfully applied to larger molecules. For more than a decade, DFT methods with all-electron basis sets have also been applied to large bioinorganic molecules. These methods allow the determination of Mossbauer parameters with impressive accuracy and have become a valuable tool for the interpretation of Mossbauer spectra. 

Ab initio quantum mechanical (QM) calculations represent approximate efforts to solve the Schrodinger equation, which describes the electronic structure of a molecule based on the Born-Oppenheimer approximation (in which the positions of the nuclei are considered fixed). It is typical for most of the calculations to be carried out at the Hartree—Fock self-consistent field (SCF) level. The major assumption behind the Hartree-Fock method is that each electron experiences the average field of all other electrons. Ab initio molecular orbital methods contain few empirical parameters. Introduction of empiricism results in the various semiempirical techniques (MNDO, AMI, PM3, etc.) that are widely used to study the structure and properties of small molecules. 

The electrostatic contribution is modelled using a Coulombic potential. The electrostatic energy is a function of the charge on the non-bonded atoms, their interatomic distance, and a molecular dielectric expression that accounts for the attenuation of electrostatic interaction by the environment (e.g. solvent or the molecule itself). Partial atomic charges can be calculated for small molecules using an ab initio or semiempirical quantum mechanics program. 

It has already been pointed out several times that electron repulsion terms play a major part in the discussion of electronic excitation energies. Within the Hartree-Fock approximation, electron interaction in closed-shell ground states can be taken care of in a reasonable way using SCF methods. In a treatment of excited states, however, configuration interaction usually has to be taken into account. (Cf. Section 1.2.4.) This can be achieved either by semiempirical methods, especially in those cases where the jr approximation is sufficient for a discussion of light absorption, or, by ab initio methods in the case of small molecules. 

Generalized Bom (GB) approach. The most common implicit models used for small molecules are the Conductor-Like Screening Model (COSMO) [77,78], the DPCM [79], the Conductor-Like Modification to the Polarized Continuum Model (CPCM) [80,81], the Integral Equation Formalism Implementation of PCM (IEF-PCM) [82] PB models, and the GB SMx models of Cramer and Truhlar [23,83-86]. The newest Minnesota solvation models are the SMD universal Solvation Model based on solute electron density [26] and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [87-89] with semiempirical terms that account for local electrostatics [90]. Further details on these methods can be found in Chapter 11 of Reference [23]. 

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