A new method for obtaining optimized parameters for semiempirical methods has been developed and applied to the modified neglect of diatomic overlap (MNDO) method. The method uses derivatives of calculated values for properties with respect to adjustable parameters to obtain the optimized values of parameters. The large increase in speed is a result of using a simple series expression for calculated values of properties rather than employing full semiempirical calculations. With this optimization procedure, the rate-determining step for parameterizing elements changes from the mechanics of parameterization to the assembling of experimental reference data.

Optimization of parameters for semiempirical methods I. Method

Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT:  B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vib...

Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

A significant modification to the additive all-atom CHARMM lipid force field (FF) is developed and applied to phospholipid bilayers with both choline and ethanolamine containing head groups and with both saturated and unsaturated aliphatic chains. Motivated by the current CHARMM lipid FF (C27 and C27r) systematically yielding values of the surface area per lipid that are smaller than experimental estimates and gel-like structures of bilayers well above the gel transition temperature, selected torsional, Lennard-Jones and partial atomic charge parameters were modified by targeting both quantum mechanical (QM) and experimental data. QM calculations ranging from high-level ab initio calculations on small molecules to semiempirical QM studies on a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer in combination with experimental thermodynamic data were used as target data for parameter optimization. These changes were tested with simulations of pure bilayers at high hydration of the following six lipids: ...

Update of the CHARMM All-Atom Additive Force Field for Lipids: Validation on Six Lipid Types

MNDO/AM1‐type parameters for twelve elements have been optimized using a newly developed method for optimizing parameters for semiempirical methods. With the new method, MNDO‐PM3, the average difference between the predicted heats of formation and experimental values for 657 compounds is 7.8 kcal/mol, and for 106 hypervalent compounds, 13.6 kcal/mol. For MNDO the equivalent differences are 13.9 and 75.8 kcal/mol, while those for AM1, in which MNDO parameters are used for aluminum, phosphorus, and sulfur, are 12.7 and 83.1 kcal/mol, respectively. Average errors for ionization potentials, bond angles, and dipole moments are intermediate between those for MNDO and AM1, while errors in bond lengths are slightly reduced.

Optimization of parameters for semiempirical methods II. Applications

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.

A new parametric quantum mechanical molecular model, AM1 (Austin Model l), based on the NDDO approximation, is described. In it the major weaknesses of MNDO, in particular failure to reproduce hydrogen bonds, have been overcome without any increase in computing time. Results for 167 molecules are reported. Parameters are currently available for C, H, 0, and N.

Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model

A general method is described for the location of transition states in reaction mechanisms. Transition states for unimolecular and bimolecular reactions can be identified. The procedure is fully automatic, once reactants and products are characterised, and no assumptions as to the geometry of the transition state or of the mechanism are necessary. Examples are given of the Cope and Claisen reactions.

Location of transition states in reaction mechanisms

Revised MNDO parameters for silicon

Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model. [Erratum to document cited in CA103(2):11627f]

A reparameterized version (PM3) of AM1 has recently been reported and the results for several hundred molecules compared with those from AM1 itself. The comparison implied that PM3 represents a significant improvement over the earlier treatment. The apparently poor performance of AM1 is, however, due to the inclusion of “AM1 results” for elements (A1,P,S) for which AM1 parameters were unavailable. If these are omitted, PM3 is seen to be only marginally better than AM1. Since this conclusion refers only to a specific set of stable molecules, it is not clear whether even this small improvement will apply to other species or studies of reactions. It is in any case insufficient to justify the confusion caused by the release of the new treatment.

Eamonn F. Healy

Papers

Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model

Location of transition states in reaction mechanisms

Revised MNDO parameters for silicon

Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model. [Erratum to document cited in CA103(2):11627f]

Comments on a comparison of AM1 with the recently developed PM3 method