Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.     

PDDG/PM3 and PDDG/MNDO: improved semiempirical methods

Two new semiempirical methods employing a Pairwise Distance Directed Gaussian modification have been developed: PDDG/PM3 and PDDG/MNDO; they are easily implemented in existing software, and yield heats of formation for compounds containing C, H, N, and O atoms with significantly improved accuracy over the standard NDDO schemes, PM5, PM3, AM1, and MNDO. The PDDG/PM3 results for heats of formation also show substantial improvement over density functional theory with large basis sets. The PDDG modifications consist of a single function, which is added to the existing pairwise core repulsion functions within PM3 and MNDO, a reparameterized semiempirical parameter set, and modified computation of the energy of formation of a gaseous atom. The PDDG addition introduces functional group information via pairwise atomic interactions using only atom-based parameters. For 622 diverse molecules containing C, H, N, and O atoms, mean absolute errors in calculated heats of formation are reduced from 4.4 to 3.2 kcal/mol and from 8.4 to 5.2 kcal/mol using the PDDG modified versions of PM3 and MNDO over the standard versions, respectively. Several specific problems are overcome, including the relative stability of hydrocarbon isomers, and energetics of small rings and molecules containing multiple heteroatoms. The internal consistency of PDDG energies is also significantly improved, enabling more reliable analysis of isomerization energies and trends across series of molecules; PDDG isomerization energies show significant improvement over B3LYP/6-31G* results. Comparison of heats of formation, ionization potentials, dipole moments, isomer, and conformer energetics, intermolecular interaction energies, activation energies, and molecular geometries from the PDDG techniques is made to experimental data and values from other semiempirical and ab initio methods.     

Computational structural determination and energy landscape analysis of the hepatic carcinogen 2-(acetylamino)fluorene

 2-(Acetylamino)fluorene (AAF), a potent mutagen and a prototypical example of the mutagenic aromatic amines, forms covalent adducts to DNA after metabolic activation in the liver. A benchmark study of AAF is presented using a number of the most widely used molecular mechanics and semiempirical computational methods and models. The results are compared to higher-level quantum calculations and to experimentally obtained crystal structures. Hydrogen bonding between AAF molecules in the crystal phase complicates the direct comparison of gas-phase theoretical calculations with experiment, so Hartree–Fock (HF) and Becke–Perdew (BP) density functional theory (DFT) calculations are used as benchmarks for the semiempirical and molecular mechanics results. Systematic conformer searches and dihedral energy landscapes were carried out for AAF using the SYBYL and MMFF94 molecular mechanics force fields; the AM1, PM3 and MNDO semiempirical quantum mechanics methods; HF using the 3-21G*and 6-31G* basis sets; and DFT using the nonlocal BP functional and double numerical polarization basis sets. MMFF94, AM1, HF and DFT calculations all predict the same planar structures, whereas SYBYL, MNDO and PM3 all predict various nonplanar geometries. The AM1 energy landscape is in substantial agreement with HF and DFT predictions; MMFF94 is qualitatively similar to HF and DFT; and the MNDO, PM3 and SYBYL results are qualitatively different from the HF and DFT results and from each other. These results are attributed to deficiencies in MNDO, PM3 and SYBYL. The MNDO, PM3 and SYBYL models may be unreliable for compounds in which an amide group is immediately adjacent to an aromatic ring. Received: 26 May 2002 / Accepted: 12 December 2002 / Published online: 14 February 2003     

The implementation of a fast and accurate QM/MM potential method in Amber

Version 9 of the Amber simulation programs includes a new semi-empirical hybrid QM/MM functionality. This includes support for implicit solvent (generalized Born) and for periodic explicit solvent simulations using a newly developed QM/MM implementation of the particle mesh Ewald (PME) method. The code provides sufficiently accurate gradients to run constant energy QM/MM MD simulations for many nanoseconds. The link atom approach used for treating the QM/MM boundary shows improved performance, and the user interface has been rewritten to bring the format into line with classical MD simulations. Support is provided for the PM3, PDDG/PM3, PM3CARB1, AM1, MNDO, and PDDG/MNDO semi-empirical Hamiltonians as well as the self-consistent charge density functional tight binding (SCC-DFTB) method. Performance has been improved to the point where using QM/MM, for a QM system of 71 atoms within an explicitly solvated protein using periodic boundaries and PME requires less than twice the cpu time of the corresponding classical simulation.     

Comparison of SCC-DFTB and NDDO-based semiempirical molecular orbital methods for organic molecules

Extensive testing of the SCC-DFTB method has been performed, permitting direct comparison to data available for NDDO-based semiempirical methods. For 34 diverse isomerizations of neutral molecules containing the elements C, H, N, and O, the mean absolute errors (MAE) for the enthalpy changes are 2.7, 3.2, 5.0, 5.1, and 7.2 kcal/mol from PDDG/PM3, B3LYP/6-31G(d), PM3, SCC-DFTB, and AM1, respectively. A more comprehensive test was then performed by computing heats of formation for 622 neutral, closed-shell H, C, N, and O-containing molecules; the MAE of 5.8 kcal/mol for SCC-DFTB is intermediate between AM1 (6.8 kcal/mol) and PM3 (4.4 kcal/mol) and significantly higher than for PDDG/PM3 (3.2 kcal/mol). Similarly, SCC-DFTB is found to be less accurate for heats of formation of ions and radicals; however, it is more accurate for conformational energetics and intermolecular interaction energies, though none of the methods perform well for hydrogen bonds with strengths under ca. 7 kcal/mol. SCC-DFTB and the NDDO methods all reproduce MP2/cc-pVTZ molecular geometries with average errors for bond lengths, bond angles, and dihedral angles of only ca. 0.01 A, 1.5 degrees , and 3 degrees . Testing was also carried out for sulfur containing molecules; SCC-DFTB currently yields much less accurate heats of formation in this case than the NDDO-based methods due to the over-stabilization of molecules containing an SO bond.     

A combined quantum chemical/molecular mechanical study of hydrogen-bonded systems

A computational approach, which involves the combination of the OPLS force field and molecular orbital MNDO , AM 1, and PM 3 methods, has been developed to describe the effects of a large, molecular mechanically simulated environment on the Hamiltonian of a quantum chemical system. To test the validity of the combined quantum mechanical/molecular mechanical (QM /MM ) potential, a systematic study of the structures and energies of neutral and charged hydrogen-bonded complexes has been carried out, including comparisons with pure semiempirical calculations and available experimental and ab initio data. It is shown that, in many cases, the hybrid QM /MM potential behaves better than do related MNDO /M , AM 1, and PM 3 methods. As a case in point, the draw-back of AM 1 favoring bifurcated H-bonded structures over single ones is not presented in the combined AM 1/OPLS scheme. Possible ways of improvement of the combined QM /MM potential are discussed. © 1992 John Wiley & Sons, Inc.     

A comparative study of various computational approaches in calculating the structure of pyridoxal 5'-phosphate (PLP)-dependent beta-lyase protein. The importance of protein environment

Various computational approaches, using molecular mechanics (Amber), semiempirical (AM1), density functional (B3LYP), and various ONIOM methods, have been comparatively investigated for the structure of Escherichia coli NifS CsdB protein. The structure of the entire monomer containing 407 amino acid residues and 579 surrounding water molecules has been optimized. The full geometry optimization in the "active site-only" approach (including only active site atoms) has been found to give the largest root-mean-square (RMS) deviation from the X-ray structure; a much better agreement has been achieved by keeping the atoms leading to the backbones of some amino acids frozen in their positions in the X-ray structure. The best agreement has been attained by including the surrounding protein in the calculations using the two-layer ONIOM (B3LYP:Amber) approach. The results presented in this study conclusively demonstrate the importance of the protein/active-site interaction on the active-site structure of the enzyme. The present theoretical study represents the largest system studied at the ONIOM level to date, containing 7992 atoms, including 84 atoms in the QM region and rest in the MM region.     

Improving description of hydrogen bonds at the semiempirical level: water–water interactions as test case

Hydrogen bonding is not well described by available semiempirical theories. This is an important restriction because hydrogen bonds represent a key feature in many chemical and biochemical processes, besides being responsible for the singular properties of water. In this study, we describe a possible solution to this problem. The basic idea is to replace the nonphysical gaussian correction functions (GCF) appearing in the core–core repulsion terms of most MNDO‐based semiempirical methods by a simple function exhibiting the correct physical behavior in the whole range of intermolecular separation distances. The parameterized interaction function (PIF) is the sum of atom‐pair contributions, each one having five adjustable parameters. In this work, the approach is used to study water–water interactions. The parameters are optimized to reproduce a reference ab initio intermolecular energy surface for the water–water dimer obtained at the MP2/aug‐cc‐pVQZ level. OO, OH, and HH parameters are reported for the PM3 method. The results of PM3‐PIF calculations remarkably improve qualitatively and quantitatively those obtained at the standard PM3 level, both for water–dimer properties and for water clusters up to the hexamer. For example, the root‐mean‐square deviation of the PM3‐PIF interaction energies, with respect to ab initio values obtained using 700 points of the water dimer surface, is only 0.47 kcal/mol. This value is much smaller than that obtained using the standard PM3 method (4.2 kcal/mol). The PM3‐PIF water dimer energy minimum (−5.0 kcal/mol) is also much closer to ab initio data (−5.0±0.01 kcal/mol) than PM3 (−3.50 kcal/mol). The method is therefore promising for the development of new semiempirical approaches as well as for application of combined quantum mechanics and molecular mechanics techniques to investigate chemical processes in water. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 572–581, 2000     

NDDO semiempirical approximations coupled with Green's function technique—a reliable approach for calculating ionization potentials

The ionization potentials of different molecules have been calculated with the outer valence Green's function (OVGF) technique, coupled with semiempirical MNDO, AM1 and PM3 methods. It is found that the OVGF method gives significantly better agreement with the experimental data than do results obtained with semiempirical calculations using Koopman's theorem including a new SAM1 and MNDO/d methods. Of the three semiempirical methods tested (MNDO, AM1, PM3) the OVGF (AM1) method gives the best agreement with experiment.     

QM:QM electronic embedding using Mulliken atomic charges: energies and analytic gradients in an ONIOM framework

An accurate first-principles treatment of chemical reactions for large systems remains a significant challenge facing electronic structure theory. Hybrid models, such as quantum mechanics:molecular mechanics (QM:MM) and quantum mechanics:quantum mechanics (QM:QM) schemes, provide a promising avenue for such studies. For many chemistries, including important reactions in materials science, molecular mechanics or semiempirical methods may not be appropriate, or parameters may not be available (e.g., surface chemistry of compound semiconductors such as indium phosphide or catalytic chemistry of transition metal oxides). In such cases, QM:QM schemes are of particular interest. In this work, a QM:QM electronic embedding model within the ONIOM (our own N-layer integrated molecular orbital molecular mechanics) extrapolation framework is presented. To define the embedding potential, we choose the real-system low-level Mulliken atomic charges. This results in a set of well-defined and unique embedding charges. However, the parametric dependence of the charges on molecular geometry complicates the energy gradient that is necessary for the efficient exploration of potential energy surfaces. We derive an efficient form for the forces where a single set of self-consistent field response equations is solved. Initial tests of the method and key algorithmic issues are discussed.     

Pyrrolizidine alkaloids necine bases: Ab initio,semiempirical, and molecular mechanics approaches to molecular properties

The structural stabilities of endo and exo conformations of retronecine and heliotridine molecules were analyzed using different ab initio, semiempirical, and molecular mechanics methods. All electron and pseudopotential ab initio calculations at the Hartree-Fock level of theory with 6-31G* and CEP-31G* basis sets provided structures in excellent agreement with available experimental results obtained from X-ray crystal structure and ¹H-NMR (nuclear magnetic resonance) studies in D₂O solutions. The exo conformations showed a greater stability for both molecules. The most significant difference between the calculations was found in the ring planarity of heliotridine, whose distortion was associated with the interaction between the O(11)H group and the C(1)-C(2) double bond as well as with a hydrogen bond between O(11)H and N(4). The discrepancy between pseudopotential and all-electron optimized geometries was reduced after inclusion of the innermost electrons of C(1), C(2), and N(4) in the core potential calculation. The MNDO, AM1, and PM3 semiempirical results showed poor agreement with experimental data. The five-membered rings were observed to be planar for AM1 and MNDO calculations. The PM3 calculations for exo-retronecine showed a greater stability than the endo conformer, in agreement with ab initio results. A good agreement was observed between MM3 and ab initio geometries, with small differences probably due to hydrogen bonds. While exo-retronecine was calculated to be more stable than the endo conformer, the MM3 calculations suggested that endo-heliotridine was slightly more stable than the exo form. © 1996 by John Wiley & Sons, Inc.     

Improved semiempirical heats of formation through the use of bond and group equivalents

Deficiencies in energetics obtained using the common semiempirical methods, AM1, PM3, and MNDO, may partly be traced to the use of pseudoatomic equivalents for conversion of molecular energies to heats of formation at 298 K. We present an alternative scheme based on the use of bond and group equivalents. Values for the 61 bond and group equivalents necessary for treatment of molecules containing the common organic elements, hydrogen, carbon, nitrogen, and oxygen have been derived. For a set of 583 neutral, closed-shell molecules mean absolute errors in AM1, PM3, and MNDO heats of formation are reduced from 6.6, 4.2, and 8.2 kcal/mol to 2.3, 2.2, and 3.0 kcal/mol, respectively. Several systematic problems are overcome in the present scheme including relative stabilities of branched hydrocarbons, energetics of conjugated systems, heats of formation of long chain hydrocarbons, and enthalpies of molecules containing multiple heteroatoms. Although the approach is restricted to molecules with well-defined functional groups, the equivalents are easy to incorporate and are chemically relevant. This revised procedure allows semiempirical methods to be used for far more reliable evaluations of heats of reactions. Estimates are made of the errors inherent in these semiempirical formalisms, arising from integral approximations and the neglect of explicit treatment of electron correlation effects, while excluding those from inadequate parameterization.     

C59H3N异构体的结构与稳定性的理论研究

分别用MNDO,AM1和PM3三种半经验方法对C59HN所有1-2,1-4和1-6氢加成物C59H3N的异构体进行几何构型全优化,结合频率分析及HF/6-31G单点能计算,确定了各异构体的基态结构及其相对稳定性,计算结果表明,C59HN氢加成物的立体选择性规律与C60和C60H2的不同,最稳定异构体不是1-2加成物,而是1-4加成的6,18-或12,15-异构体,次稳定异构体为1-2加成物,三种半经验方法计算得到的两者能量差为13～15kJ/mol,N原子取代碳笼骨架C原子后,改变了碳笼氢加成物的立体选择性规律.     

De novo prediction of ground state multiplicity and structural isomerism for transition metal complexes

Prediction of the ground state geometries and multiplicities for 33 transition metal tetrachlorides has been carried out using two different levels of quantum mechanics: semiempirical and density functional theory. All data regarding geometry and spin state provided by both computational methods were compared with experimental data when available. The calculations were performed for all possible spin multiplicities. The most important geometries for coordination number four (tetrahedral, square-planar, dodecahedral, and disphenoidal), as well as less symmetric structural isomers, were evaluated. A match between both computational methods in terms of predicted ground state multiplicity and geometry was found for 26 species, which translated into almost 80% agreement. Even though the PM3(tm) geometry prediction protocol involved more steps for isolating a feasible global minimum, the aggregate of these calculations was still orders of magnitude faster than DFT calculations using extended basis sets. The calculations indicate that caution is needed in the application of the PM3(tm) method to very high-spin transition metal complexes, but point to the suitability of very rapid semiempirical methods for reliable prediction of structural and ‘spin’ isomers, and hence their use in an efficient de novo design protocol for transition metal complexes.     

Toward accurate barriers for enzymatic reactions: QM/MM case study on p-hydroxybenzoate hydroxylase

The hydroxylation reaction catalyzed by p-hydroxybenzoate hydroxylase has been investigated by quantum mechanical/molecular mechanical (QM/MM) calculations at different levels of QM theory. The solvated enzyme was modeled (approximately 23,000 atoms in total, 49 QM atoms). The geometries of reactant and transition state were optimized for ten representative pathways using semiempirical (AM1) and density functional (B3LYP) methods as QM components. Single-point calculations at B3LYP/MM optimized geometries were performed with local correlation methods [LMP2, LCCSD(T0)] and augmented triple-zeta basis sets. A careful validation of the latter approach with regard to all computational parameters indicates convergence of the QM contribution to the computed barriers to within approximately 1 kcal mol(-1). Comparison with the available experimental data supports this assessment.