Theory and range of modern semiempirical molecular orbital methods

Semiempirical molecular orbital methods have a long history. They serve to tackle large systems and complicated processes beyond the reach of ab initio or density functional methods. Although their setup is derived from Hartree–Fock theory, the design of approximate energy expressions and the empirical parameters are used to achieve higher accuracy than the underlying ab initio theory. In this way the effect of larger basis sets or correlation can be partially simulated. All widely used semiempirical methods establish their accuracy by error statistics for molecular properties with experimental and high-level ab initio or density functional theory calculations as a reference. Their computational efficiency makes them suitable for the study of biochemical systems and solid materials. The present review presents a variety of applications which demonstrate the need for and success of semiempirical methods.     

Modeling lanthanide complexes: sparkle/AM1 parameters for ytterbium (III)

The Sparkle/AM1 model is extended to ytterbium (III) complexes. Thus, a set of 15 complexes, with various representative ligands, chosen to be representative of all complexes of high crystallographic quality (R-factor <0.05 A) in the Cambridge Crystallographic Database, and which possess oxygen and/or nitrogen as coordinating atoms, was used as the training set. In the validation procedure we added 32 more high quality crystallographic structures. For the 47 complexes, the Sparkle/AM1 unsigned mean error for all interatomic distances between the Yb(III) ion and the ligand atoms of the first sphere of coordination is 0.07 A, similar to present-day ab initio/ECP geometry prediction accuracies, and potentially useful for luminescent complex design while being hundreds of times faster.     

Exploring the parameter space of the coarse‐grained UNRES force field by random search: Selecting a transferable medium‐resolution force field

We explored the energy‐parameter space of our coarse‐grained UNRES force field for large‐scale ab initio simulations of protein folding, to obtain good initial approximations for hierarchical optimization of the force field with new virtual‐bond‐angle bending and side‐chain‐rotamer potentials which we recently introduced to replace the statistical potentials. 100 sets of energy‐term weights were generated randomly, and good sets were selected by carrying out replica‐exchange molecular dynamics simulations of two peptides with a minimal α‐helical and a minimal β‐hairpin fold, respectively: the tryptophan cage (PDB code: 1L2Y) and tryptophan zipper (PDB code: 1LE1). Eight sets of parameters produced native‐like structures of these two peptides. These eight sets were tested on two larger proteins: the engrailed homeodomain (PDB code: 1ENH) and FBP WW domain (PDB code: 1E0L); two sets were found to produce native‐like conformations of these proteins. These two sets were tested further on a larger set of nine proteins with α or α + β structure and found to locate native‐like structures of most of them. These results demonstrate that, in addition to finding reasonable initial starting points for optimization, an extensive search of parameter space is a powerful method to produce a transferable force field. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Efficient newton–raphson/singular value decomposition-based optimization scheme with dynamically updated critical condition number for rapid convergence of weighted histogram analysis method equations

Selection of the successful optimization strategy is an essential part of solving numerous practical problems yet often is a nontrivial task, especially when a function to be optimized is multidimensional and involves statistical data. Here we propose a robust optimization scheme, referred to as NR/SVD-Cdyn, which is based on a combination of the Newton–Raphson (NR) method along with singular value decomposition (SVD), and demonstrate its performance by numerically solving a system of the weighted histogram analysis method equations. Our results show significant improvement over the direct iteration and conventional NR optimization methods. The proposed scheme is universal and could be used for solving various optimization problems in the field of computational chemistry such as parameter fitting for the methods of molecular mechanics and semiempirical quantum-mechanical methods. © 2019 Wiley Periodicals, Inc.     

MSINDO parameterization for third‐row transition metals

The recently developed MSINDO version of the semiempirical SCF MO method SINDO1 has been parameterized for third‐row transition metals Sc to Zn. The set of reference data used for the previous parameterization of SINDO1 has been substantially increased by incorporating results of recent experiments and first‐principles calculations. A comparison of calculated heats of formation, geometries, ionization potentials, and dipole moments with literature values for more than 200 gas phase molecules is presented. The accuracy of the modified MSINDO version achieved for heats of formation and bond lengths has been considerably improved compared to SINDO1. Small clusters of transition metals and metal oxides were included in the parameterization to ensure accurate results for studies of larger systems. The application of the method to small transition metal complexes that were not included in the parameterization shows that the optimized parameters are transferable to other compounds. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 861–887, 2001     

Assessing the quality of absolute hydration free energies among CHARMM‐compatible ligand parameterization schemes

Multipurpose atom‐typer for CHARMM (MATCH), an atom‐typing toolset for molecular mechanics force fields, was recently developed in our laboratory. Here, we assess the ability of MATCH‐generated parameters and partial atomic charges to reproduce experimental absolute hydration free energies for a series of 457 small neutral molecules in GBMV2, Generalized Born with a smooth SWitching (GBSW), and fast analytical continuum treatment of solvation (FACTS) implicit solvent models. The quality of hydration free energies associated with small molecule parameters obtained from ParamChem, SwissParam, and Antechamber are compared. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, these automated parameterization schemes with GBMV2 and GBSW demonstrate reasonable agreement with experimental hydration free energies (average unsigned errors of 0.9–1.5 kcal/mol and R² of 0.63–0.87). GBMV2 and GBSW consistently provide slightly more accurate estimates than FACTS, whereas Antechamber parameters yield marginally more accurate estimates than the current generation of MATCH, ParamChem, and SwissParam parameterization strategies. Modeling with MATCH libraries that are derived from different CHARMM topology and parameter files highlights the importance of having sufficient coverage of chemical space within the underlying databases of these automated schemes and the benefit of targeting specific functional groups for parameterization efforts to maximize both the breadth and the depth of the parameterized space. © 2013 Wiley Periodicals, Inc.     

The Analytical Parametrization of Fusion Barrier by Using the Skyrme Energy-Density Function Model

Using the skyrme energy density formalism, a pocket formula is introduced for barrier heights and positions of 95 fusion reactions (48 ≤ Z_PZ_T ≤ 1520) with respect to the charge and mass numbers of the interacting nuclei. It is shown that the parameterized values of RB and VB are able to reproduce the corresponding experimental data with good accuracy. Moreover, the absolute errors of our formulas are less than those obtained using the analytical parametrization forms of the fusion barrier based on the proximity versions. The ability of the parameterized forms of the barrier heights and its positions to reproduce the experimental data of the fusion cross section have been analyzed using the Wong model.     

A fast and accurate algorithm for solving linear systems associated with a class of negative matrix

A class of negative matrices including Vandermonde-like matrices tends to be extremely ill-conditioned, and linear systems associated with this class of matrices appear in the polynomial interpolation problems. In this article, we present a fast and accurate algorithm with $O(n^2)$ complexity to solve the linear systems whose coefficient matrices belong to the class of negative matrix. We show that the inverse of any such matrix is generated in a subtraction-free manner. Consequently, the solutions of linear systems associated with the class of negative matrix are accurately determined by parameterization matrices of coefficient matrices, and a pleasantly componentwise forward error is provided to illustrate that each component of the solution is computed to high accuracy. Numerical experiments are performed to confirm the claimed high accuracy.