Can semi-empirical models describe HCl dissociation in water?

We discuss the failure of commonly used AM1 and PM3 semiempirical methods to correctly describe acid dissociation. We focus our analysis on HCl because of its physicochemical importance and its relevance in atmospheric chemistry. The structure of non-dissociated and dissociated HCl – (H₂O) _n clusters is accounted for. The very bad results obtained with PM3 (and also with AM1) are related to large errors in gas-phase proton affinity of water and gas-phase acidity of HCl. Indeed, estimation of pKa values shows that neither AM1 nor PM3 are able to predict HCl dissociation in liquid water since HCl is found to be a weaker acid than H₃O⁺. We have proposed in previous works a modified PM3 approach (PM3-MAIS) adapted to intermolecular calculations. It is derived from PM3 by reparameterization of the core–core functions using ab initio data. Since parameters for H–Cl and O–Cl core–core interactions were not yet available, we have carried out the corresponding optimization. Application of the PM3-MAIS method to HCl dissociation in HCl–(H₂O) _n clusters leads to a huge improvement over PM3 results. Though the method predicts a slightly overestimated HCl acidity in water environment, the overall agreement with ab initio calculations is very satisfying and justifies efforts to develop new semiempirical methods.     

Prediction of geometries and interaction energies of complexes formed by small molecules using semiempirical and ab initio methods

The accuracy of the semiempirical quantum mechanics methods (AM1 and PM3), and the ab initio methods (6-31G^** and MP2/6-31G^**) in predicting intermolecular geometries and interaction energies have been evaluated by detailed studies of 17 bimolecular complexes formed by small molecules. Comparisons between calculated and experimental geometries for 12 complexes are presented. It was found that AM1 gave reasonably good predictions of the geometries of complexes such as CH₄ · CH₄, which have very weak interactions, but it is not as good as other methods in predicting intermolecular geometry for complexes where hydrogen bonding interactions play an important role. This is consistent with its inability to reproduce the charge transfer in the formation of hydrogen bonds in these complexes.

PM3 is able to predict intermolecular geometries for most complexes, including those with hydrogen bonding; its major flaw is its tendency to overestimate the strength of the interactions between hydrogen atoms. Care should be taken therefore in using PM3 to study complicated molecular systems with multiple hydrogen atom interactions and the method's weakness in handling complexes in which electrostatic forces are important should also be noted.

Among ab initio methods, both the 6-31G^** and the MP2/6-31G^** were found to outperform AM1 and PM3 in prediction of intermolecular geometry. Both of these ab initio methods showed excellent consistency in geometry prediction for most of the complexes studied, although MP2/6-31G^** is better than 6-31G^**. It is noted that the MP2/6-31G^** did not produce the correct geometry for the CO₂· HF complex.

For 12 complexes for which experimental geometry data are available, AM1, PM3, 6-31G^**, and MP2/6-31G^** successfully predicted the geometry in 10, 12, 12, and 11 cases, respectively. The average errors given by AM1 in the predicted intermolecular distances were 0.264, 0.272, 0.091, and 0.061 Å, respectively. In comparison to the ab initio methods, AM1 and PM3 commonly underestimated the molecular interaction energy in such complexes by ˜ 1–2 kcal mol⁻¹.     

Semi-empirical molecular orbital methods including dispersion corrections for the accurate prediction of the full range of intermolecular interactions in biomolecules

Semi-empirical calculations including an empirical dispersive correction are used to calculate intermolecular interaction energies and structures for a large database containing 156 biologically relevant molecules (hydrogen-bonded DNA base pairs, interstrand base pairs, stacked base pairs and amino acid base pairs) for which MP2 and CCSD(T) complete basis set (CBS) limit estimates of the interaction energies are available. The dispersion corrected semi-empirical methods are parameterised against a small training set of 22 complexes having a range of biologically important non-covalent interactions. For the full molecule set (156 complexes), compared to the high-level ab initio database, the mean unsigned errors of the interaction energies at the corrected semi-empirical level are 1.1 (AM1-D) and 1.2 (PM3-D) kcal mol(-1), being a significant improvement over existing AM1 and PM3 methods (8.6 and 8.2 kcal mol(-1)). Importantly, the new semi-empirical methods are capable of describing the diverse range of biological interactions, most notably stacking interactions, which are poorly described by both current AM1 and PM3 methods and by many DFT functionals. The new methods require no more computer time than existing semi-empirical methods and therefore represent an important advance in the study of important biological interactions.     

Computational analysis of binding affinity and neural response at the l-alanine receptor

Summary A model of analogue-receptor binding is developed for the l-alanine receptor in the channel catfish using the AM1-SM2 and ab initio SCRF computational methods. Besides interactions involving the zwitterionic moiety of the amino acid analogue and complementary subsites on the receptor, the model suggests the presence of a hydrophobic pocket with dispersion interactions between the receptor and the residue on the amino acid analogue. Conformational analysis suggests not only a small compact active site on the receptor, but also that the analogues with the highest affinity occupy nearly identical regions of space. Although the binding interaction is dominated by the ionic terms, AM1-SM2 calculations indicate that free energy terms associated with cavity formation, solvent reorganization, and dispersion interactions can be correlated to activation and neural response. From a consideration of this model, molecular features of the analogues that are important for binding and neural response were deduced and other analogues or ligands were developed and tested.     

Theoretical studies on the structure and electronic properties of aryl sulfides and sulfones

Molecular orbital calculations are reported on the structure and electronic properties of diphenyl sulfide using both semiempirical and ab initio methods. Neither the MNDO nor AM1 methods give satisfactory structures, but better results are obtained with the PM3 method. At the ab initio level, the 4-31G basis set with polarization functions on sulfur alone (4-31G/S*) gives comparable results to those obtained with the 6-31G** basis set. The corresponding bond lengths and angles at the sulfur atom of 4-aminophenyl-4′-nitrophenyl sulfide and related derivatives of diphenyl sulfone, diphenyl disulfide, and phenylthiosulfonate calculated at the 4-31 G/S* level show a good correlation with crystallographic data where available. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 141–147, 1998     

Structures and energies of D-galactose and galabiose conformers as calculated by ab initio and semiempirical methods

Optimized geometries and total energies of some conformers of alpha- and beta-D-galactose have been calculated using the RHF/6-31G* ab initio method. Vibrational frequencies were computed at the 6-31G* level for the conformers that favor internal hydrogen bonding, in order to evaluate their enthalpies, entropies, Gibbs free energies, and then their structural stabilities. The semiempirical AM1, PM3, MNDO methods have also been performed on the conformers GG, GT, and TG of alpha- and beta-D-galactose. In order to test the reliability of each semiempirical method, the obtained structures and energies from the AM1, PM3, and MNDO methods have been compared to those achieved using the RHF/6-31G* ab initio method. The MNDO method has not been investigated further, because of the large deviation in the structural parameters compared with those obtained by the ab initio method for the galactose. The semiempirical method that has yielded the best results is AM1, and it has been chosen to perform structural and energy calculations on the galabiose molecule (the disaccharides constituted by two galactose units alpha 1,4 linked). The goal of such calculations is to draw the energy surface maps for this disaccharide. To realize each map, 144 different possible conformations resulting from the rotations of the two torsional angles psi and phi of the glycosidic linkage are considered. In each calculation, at each increment of psi and phi, using a step of 30 degrees from 0 to 330 degrees, the energy optimization is employed. In this article, we report also calculations concerning the galabiose molecule using different ab initio levels such as RHF/6-31G*, RHF/6-31G**, and B3Lyp/6-31G*.     

Theoretical study of C24N4 molecule

Both ab initio 6-31G, 3-21G and STO-3G basis sets and semiempirical PM3 and AM1 molecular orbital calculations are carried out on the C₂₄N₄ molecule of the T_d symmetry group. Results on the fully optimized structure which constrained T_d symmetry, molecular orbitals and vibrational frequency were obtained by both ab initio and semiempirical methods. The binding energy and various thermodynamic properties were also calculated via the PM3 and AM1 semiempirical methods. All the evidence of this work proves that the C₂₄N₄ molecule is stable and that its four six-membered rings with a remarkable delocalized C…C bond are similar to the related rings in the C₆₀ buckminsterfullerene structure.     

Fourier transform infrared and Raman spectra. Semi empirical AM1 and PM3; MP2/DZV and DFT/B3LYP-6-31G(d) ab initio calculations for dimethylterephthalate (DMT)

Fourier transform infrared and Raman spectra of dimethylterephthalate (DMT), as microcrystalline powder, have been investigated. The vibrational spectra were calculated using the AM1 and PM3 semi empirical procedures, and the M?ller-Plesset (MP2/DZV), and the Becke-Lee, Yang and Parr gradient-corrected correlation functional: B3LYP/6-31G(d) ab initio calculations. On this basis, and assisted with the FT-IR and Raman spectra of the terephthalic acid, an assignment of the vibrational spectra of dimethylterephthalate was proposed. In the calculations, remarkable differences concerning the assignments of the vibrational spectra were noted between the AM1 and PM3 methods. Also, the ab initio procedure shows differences in interpreting the spectra compared with the semi empiric procedures, and among themselves. Calculated geometrical parameters were compared with the experimental values of dimethylterephthalate, diethylterephthalate and terephthalic acid.     

Ab initio and semiempirical study of structure and electronic spectra of hydroxy substituted naphthoquinones

The geometries of hydroxy derivatives of 1,4-naphthoquinone (NQ), viz., 2-hydroxy-1,4-naphthoquinone (2HNQ), 5-hydroxy-1,4-naphthoquinone (5HNQ), and 5,8-dihydroxy-1,4-naphthoquinone (DHNQ), have been optimized using the semiempirical and ab initio theoretical methods. Semiempirical methods used for the optimization are Austin Model 1 (AM1) and Zerner's Intermediate Neglect of Differential Overlap/1(ZINDO/1). For ab initio calculations the 6-31G* basis set is used. The electronic spectra of 1,4-naphthoquinone and its hydroxy derivatives are calculated using the semiempirical Zerner's Intermediate Neglect of Differential Overlap/Spectroscopy (ZINDO/S) method employing the geometries optimized at AM1, ZINDO/1 and ab initio levels and compared with their electronic absorption spectra measured by us. For hydroxy substituted systems, such calculations for spectral assignments are made for the first time. It is found that though the predictions of the three theoretical methods for the geometries are similar, the predictions of the ZINDO/S method using the ZINDO/1 optimized geometries, are better for the transition wavelengths in the visible region of the hydroxy substituted naphthoquinones, especially for 5HNQ and DHNQ.     

A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Comparison of AM1 and PM3 semiempirical to ab initio methods in the study of Diels-Alder reactions of butadiene and cyclopentadiene with cyanoethylenes

Assuming a concerted synchronous mechanism with one transition state of the Diels-Alder reactions, the structures of the transition states and the activation energies for the reactions of butadiene and cyclopentadiene with cyanoethylenes were calculated by AM1 and PM3 semiempirical methods. The structural parameters were compared with those obtained by high level Gaussian calculations, whereas the activation energies were compared both with the ab initio calculations and those obtained experimentally. The structural properties calculated with PM3 methods are in general in better agreement with the ab initio calculations. The low level ab initio calculations are in many cases worse than the semiempirical methods. All predicted activation energies with both semiempirical methods are up to 300% higher than the experimental values. The predicted reactivity is also opposite to the experimental data. Only the very high level Gaussian calculations are in good correlation with experimental results. The predicted selectivity of the reaction is also opposite to the experimental facts. Two explanations are offered for this discrepancy: AM1 and PM3 methods cannot handle the calculation of the concerted Diels-Alder transition states and are not recommended to be used for that purpose, or this Diels-Alder reaction is not concerted but is stepwise.     

A theoretical analysis of the structure and electronic properties of 2-nitrophenylcyanate and 2-nitrophenylthiocyanate

Molecular orbital calculations are reported on the structure and electronic properties of both 2-nitrophenylcyanate and 2-nitrophenylthiocyanate using both the semiempirical AM1 and PM3 methods and the ab initio 3-21G and 6-31G** basis sets. The resulting structures are compared with crystallographic data where available. The marked difference in biological activity observed between the two molecules appears to be attributable to large differences in their electronic properties rather than to any geometric factors. © 1996 John Wiley & Sons, Inc.     

Theoretical studies on the hydration of formic acid by ab initio and ABEEMσπ fluctuating charge model

The interaction between formic acid (FA) and water was systemically investigated by atom-bond electronegativity equalization method fused into molecular mechanics (ABEEMσπ/MM) and ab initio methods. The geometries of 20 formic acid–water complexes (FA–water) were obtained using B3LYP/aug-cc-pVTZ level optimizations, and the energies were determined at the MP2/aug-cc-pVTZ level with basis set superposition error (BSSE) and zero-point vibrational energy (ZPVE) corrections. The ABEEMσπ potential model gives reasonable properties of these clusters when compared with the present ab initio data. For interaction energies, the root mean square deviation is 0.74 kcal/mol, and the linear coefficient reaches 0.993. Next, FA in aqueous solution was also studied. The hydrogen-bonding pattern due to the interactions with water has been analyzed in detail. Furthermore, the ABEEMσπ charges changed when H₂O interacted with the FA molecule, especially at the sites where the hydrogen bonds form. These results show that the ABEEMσπ fluctuating charge model is fine giving the overall characteristic hydration properties of FA–water systems in good agreement with the high-level ab initio calculations.     

Semiempirical MO methods: the middle ground in molecular modeling

Semiempirical methods occupy an important middle ground between molecular mechanics and ab initio MO calculations in the repertoire of methods available for studying the structures, properties and reactions of molecules. They have a unique combination of speed and generality which makes it possible to study many chemical systems which are beyond the reach of classical force fields and too large for ab initio MO methods. Indeed, semiempirical calculations are often the first computational technique to be applied to a chemical problem. Three examples where semiempirical MO calculations have provided significant mechanistic insight are the cylcopropylcarbinyl cation, porphyrin structure and dynamics, and the role of C---H hydrogen bonds in polymer miscibility. In each case Semiempirical calculations have been at the fore, and their results have been generally confirmed by subsequent ab initio calculations and experiment.     

Ab initio and RRKM study of the HCN/HNC elimination channels from vinyl cyanide

Ab initio CCSD and CCSD(T) calculations with the 6-311+G(2d,2p) and the 6-311++G(3df,3pd) basis sets were carried out to characterize the vinyl cyanide (C(3)H(3)N) dissociation channels leading to hydrogen cyanide (HCN) and its isomer hydrogen isocyanide (HNC). Our computations predict three elimination channels giving rise to HCN and another four channels leading to HNC formation. The relative HCN/HNC branching ratios as a function of internal energy of vinyl cyanide were computed using RRKM theory and the kinetic Monte Carlo method. At low internal energies (120 kcal/mol), the total HCN/HNC ratio is about 14, but at 148 kcal/mol (193 nm) this ratio becomes 1.9, in contrast with the value 124 obtained in a previous ab initio/RRKM study at 193 nm (Derecskei-Kovacs, A.; North, S. W. J. Chem. Phys.1999, 110, 2862). Moreover, our theoretical results predict a ratio of rovibrationally excited acetylene over total acetylene of 3.3, in perfect agreement with very recent experimental measurements (Wilhelm, M. J.; Nikow, M.; Letendre, L.; Dai, H.-L. J. Chem. Phys.2009, 130, 044307).     

Ab initio rotation-vibration spectra of HCN and HNC

We have calculated an ab initio HCN/HNC linelist for all transitions up to J= 25 and 18000 cm(-1) above the zero point energy. This linelist contains more than 200 million lines each with frequencies and transition dipoles. The linelist has been calculated using our semi-global HCN/HNC VQZANO + PES and dipole moment surface, which were reported in van Mourik et al. (J. Chem. Phys. 115 (2001) 3706). With this linelist we synthesise absorption spectra of HCN and HNC at 298 K and we present the band centre and band transition dipoles for the bands which are major features in these spectra. Several of the HCN bands and many of the HNC bands have not been previously studied. Our line intensities reproduce via fully ab initio methods the unusual intensity structure of the HCN CN stretch fundamental (00(0)1) for the first time and also the forbidden (02(2)0) HCN bending overtone. We also compare the J = 1-->0 pure rotational transition dipole in the HCN/HNC ground and vibrationally excited states with experimental and existing ab initio results.     

Knoevenagel condensation of cyclic ketones with benzoylacetonitrile and N,N′-dimethylbarbituric acid. Application of sterically hindered condensation products in the synthesis of spiro and dispiropyrans by hetero-Diels-Alder reactions

Inverse-electron demand Diels-Alder cycloadditions of sterically hindered cycloalkylidene derivatives of benzoylacetonitrile and N,N′-dimethylbarbituric acid with enol ethers, cyclic enol ethers and also sterically hindered cycloalkylidenecycloalkanes were investigated. New spiro, dispirodihydropyrans, spirouracils, and dispirouracils were obtained. To confirm the experimental results, frontier orbital HOMO and LUMO energies of heterodienes and dienophiles were calculated by semi-empirical AM1, PM3 methods and ab initio Hartree-Fock calculations.