Several modifications that have been made to the NDDO core-core interaction term and to the method of parameter optimization are described. These changes have resulted in a more complete parameter optimization, called PM6, which has, in turn, allowed 70 elements to be parameterized. The average unsigned error (AUE) between calculated and reference heats of formation for 4,492 species was 8.0 kcal mol−1. For the subset of 1,373 compounds involving only the elements H, C, N, O, F, P, S, Cl, and Br, the PM6 AUE was 4.4 kcal mol−1. The equivalent AUE for other methods were: RM1: 5.0, B3LYP 6–31G*: 5.2, PM5: 5.7, PM3: 6.3, HF 6–31G*: 7.4, and AM1: 10.0 kcal mol−1. Several long-standing faults in AM1 and PM3 have been corrected and significant improvements have been made in the prediction of geometries.

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Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements.

It is demonstrated that semiempirical methods give electrostatic potential (ESP) derived atomic point charges that are in reasonable agreement with ab initio ESP charges. Furthermore, we find that MNDO ESP charges are superior to AM1 ESP charges in correlating with ESP charges derived from the 6-31G* basis set. Thus, it is possible to obtain 6-31G* quality point charges by simply scaling MNDO ESP charges. The charges are scaled in a linear (y = Mx) manner to conserve charge. In this way researchers desiring to carry out force field simulations or minimizations can obtain charges by using MNDO, which requires much less computer time than the corresponding 6-31G* calculation.

Atomic charges derived from semiempirical methods

An LCAO-MO-SCF-CI model along the lines introduced by Del Bene and Jaffe is developed that is capable of reproducing the better identified observed spectra of nitrogen heterocycles with a rms error of ∼ 1000 cm−1. The model is applied to the spectra of pyrrole, benzene, pyridine, the diazines, symmetric triazine and symmetric tetrazine. The benzene and pyridine spectra are reproduced nearly exactly. The band observed in pyrrole at ∼ 6.5 eV is calculated as two bands at ∼ 6.5 eV, but they are assigned π→σ
* and not π→π. No evidence is found for the low lying 1
B
2g
 in pyrazine, reported at ∼ 30400 cm−1 in pure crystals. The lowest excited singlet of sym. triazine is calculated as 1
E″ (n→π
*), not 1
A″2 (n→π), in agreement with a recent interpretation of Fischer and Small. Several bands are reassigned, and the electronic nature of the transitions discussed. Naphthalene and quinoxaline are examined to insure that no large drift of results are met with molecules of other sizes. Comparison of eigenvalues with molecular ionization potentials is made. Here the numerical agreement appears satisfactory for the first few ionization potentials only.

An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines

Modern semiempirical methods are of sufficient accuracy when used in the modeling of molecules of the same type as used as reference data in the parameterization. Outside that subset, however, there is an abundance of evidence that these methods are of very limited utility. In an attempt to expand the range of applicability, a new method called PM7 has been developed. PM7 was parameterized using experimental and high-level ab initio reference data, augmented by a new type of reference data intended to better define the structure of parameter space. The resulting method was tested by modeling crystal structures and heats of formation of solids. Two changes were made to the set of approximations: a modification was made to improve the description of noncovalent interactions, and two minor errors in the NDDO formalism were rectified. Average unsigned errors (AUEs) in geometry and ΔHf for PM7 were reduced relative to PM6; for simple gas-phase organic systems, the AUE in bond lengths decreased by about 5 % and the AUE in ΔHf decreased by about 10 %; for organic solids, the AUE in ΔHf dropped by 60 % and the reduction was 33.3 % for geometries. A two-step process (PM7-TS) for calculating the heights of activation barriers has been developed. Using PM7-TS, the AUE in the barrier heights for simple organic reactions was decreased from values of 12.6 kcal/mol-1 in PM6 and 10.8 kcal/mol-1 in PM7 to 3.8 kcal/mol-1. The origins of the errors in NDDO methods have been examined, and were found to be attributable to inadequate and inaccurate reference data. This conclusion provides insight into how these methods can be improved.

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Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters.

Quantitative structure-activity and structureproperty relationship (QSAR/QSPR) studies are unquestionably of great importance in modern chemistry and biochemistry. The concept of QSAR/QSPR is to transform searches for compounds with desired properties using chemical intuition and experience into a mathematically quantified and computerized form. Once a correlation between structure and activity/property is found, any number of compounds, including those not yet synthesized, can be readily screened on the computer in order to select structures with the properties desired. It is then possible to select the most promising compounds to synthesize and test in the laboratory. Thus, the QSAR/QSPR approach conserves resources and accelerates the process of development of new molecules for use as drugs, materials, additives, or for any other purpose. While it is not easy to find successful structureactivity/property correlations, the recent exponential growth in the number of papers dealing with QSAR/ QSPR studies clearly demonstrates the rapid progress in this area. To obtain a significant correlation, it is crucial that appropriate descriptors be employed, whether they are theoretical, empirical, or derived from readily available experimental characteristics of the structures. Many descriptors reflect simple molecular properties and thus can provide insight into the physicochemical nature of the activity/ property under consideration. Recent progress in computational hardware and the development of efficient algorithms has assisted the routine development of molecular quantummechanical calculations. New semiempirical methods supply realistic quantum-chemical molecular quantities in a relatively short computational time frame. Quantum chemical calculations are thus an attractive source of new molecular descriptors, which can, in principle, express all of the electronic and geometric properties of molecules and their interactions. Indeed, many recent QSAR/QSPR studies have employed quantum chemical descriptors alone or in combination with conventional descriptors. Quantum chemistry provides a more accurate and detailed description of electronic effects than empirical methods.1 Quantum chemical methods can be applied to quantitative structure-activity relationships by direct derivation of electronic descriptors from the molecular wave function. In many cases it has been established that errors due to the approximate nature of quantum-chemical methods and the neglect of the solvation effects are largely transferable within structurally related series; thus, relative values of calculated descriptors can be meaningful even though their absolute values are not directly applicable.2 Moreover, electronic descriptors derived from the molecular wave function can be also partitioned on the basis of atoms or groups, allowing the description of various molecular regions separately. Most work employing quantum chemical descriptors has been carried out in the field of QSAR rather than QSPR, i.e. the descriptors have been correlated with biological activities such as enzyme inhibition activity, hallucinogenic activity, etc.3-6 In part this has been because, historically, the search for quantitative relationships with chemical structure started with the development of theoretical drug design methods. Quantum-chemical descriptors have also been reported to correlate the reactivity of organic compounds, octanol/water partition coefficients, chromatographic retention indices, and various physical properties of molecules.7-11 The present article reviews applications of quantum chemical descriptors in the development of QSAR/QSPR dealing with the chemical, physical, biochemical, and pharmacological properties of compounds.

http://depa.fquim.unam.mx/amyd//archivero/TrabajoFINAL2013-1_21514.pdf

Quantum-Chemical Descriptors in QSAR/QSPR Studies

A new approximate self‐consistent‐field method for the determination of molecular orbitals for all valence electrons of a molecule is proposed. This method features neglect of differential overlap in all electron‐interaction integrals except those involving one center only. The parameters involved in the calculation are generally obtained semi‐empirically. The new method is known as the Intermediate Neglect of Differential Overlap (INDO) method, and may be regarded as an improvement over the CNDO method proposed in Part I, in that atomic term‐level splittings and unpaired spin distributions are better accommodated. Calculations on geometries of AB2 and AB3 molecules are reported to substantiate the proposed method, and calculated unpaired spin distributions for methyl and ethyl radicals are discussed.

Approximate Self‐Consistent Molecular‐Orbital Theory. V. Intermediate Neglect of Differential Overlap

Molecular orbital theory of the electronic structure of organic compounds. II. Spin densities in paramagnetic species

Molecular‐Orbital Theory of Geometry and Hyperfine Coupling Constants of Fluorinated Methyl Radicals

The effect of contaminating spin components in spin‐unrestricted valence‐electron molecular‐orbital wavefunctions calculated at the INDO level of approximation is considered with reference to the calculation of unpaired spin populations and isotropic hyperfine coupling constants in organic molecules.

Paul A. Dobosh

Papers

Approximate Self‐Consistent Molecular‐Orbital Theory. V. Intermediate Neglect of Differential Overlap

Molecular orbital theory of the electronic structure of organic compounds. II. Spin densities in paramagnetic species

Molecular‐Orbital Theory of Geometry and Hyperfine Coupling Constants of Fluorinated Methyl Radicals

Spin Contamination in Spin-Unrestricted INDO Molecular-Orbital Wavefunctions

Steroids and Steroidases. XVI.' An Evaluation of Synthetic Routes to Variously C-17-Substituted A5-3-Ketosteroids