Semiempirical treatment of electrostatic potentials and partial charges in combined quantum mechanical and molecular mechanical approaches

A semiempirical treatment of electrostatic potentials and partial charges is presented. These are the basic components needed for the evaluation of electrostatic interaction energies in combined quantum mechanical and molecular mechanical approaches. The procedure to compute electrostatic potentials uses AM1 and MNDO wave functions and is based on one previously suggested by Ford and Wang. It retains the NDDO approximation and is thus both easy to implement and computationally efficient. Partial atomic charges are derived from a semiempirical charge equilibration model, which is based on the principle of electronegativity equalization. Large sets of ab initio restricted Hartee-Fock (RHF/6-31G*) reference data have been used to calibrate the semiempirical models. Applying the final parameters (C, H, N, O), the ab initio electrostatic potentials are reproduced with an average accuracy of 20% (AM1) and 25% (MNDO), respectively, and the ab initio potential derived charges normally to within 0.1 e. In most cases our parameterized models are more accurate than the much more expensive quasi ab initio techniques, which employ deorthogonalized semiempirical wave functions and have generally been preferred in previous applications. © 1996 John Wiley & Sons, Inc.     

Conformational energies and rotational barriers in 3-methyl-1-butene and 1-butene: An ab initio and molecular mechanics study

The calculated result obtained with MM2(87) for the rotation of the isopropyl group in 3-methyl-1-butene is not in agreement with experimental data. In order to reparametrize the C_sp2-C_sp3-C_sp-C_sp3 torsional angle, 3-methyl-1-butene and 1-butene have been studied by molecular mechanics (MM2(87)) and ab initio (MP2/6-31G* and MP3/6-31G*) calculations. The reparametrization of the torsional angle gives calculated results from MM2(87) in agreement with experimental data and ab initio calculations for both 3-methyl-1-butene and 1-butene. The calculated barriers for the rotation of alkyl groups in alkylbenzenes are improved with these new parameters.     

An ab initio and molecular mechanical investigation of ureas and amide derivatives

Ab initio molecular orbital theory with the 6-31G* basis set has been used to investigate the geometries and preferred conformations for urea, derivatives of urea, and a few complicated amide derivatives. The results from the ab initio calculations provide insight into the gas-phase rotational barrier about the C? N bond and have been used to generate parameters for the MM2(87) molecular mechanics program. When applicable, theoretical structures are compared with corresponding previously reported experimental geometries. Urea is predicted to be nonplanar with pyramidal amino groups.     

Molecular mechanics (MM3) parameterization of hydroxylamine and methyl derivatives

Based on results of electron diffraction, gas phase infrared spectroscopy (IR), and MP2/6-31 + G* ab initio calculations, a set of molecular mechanics (MM3) parameters was developed for molecules containing the N(sp³)—O(sp³) moiety. Using this set of parameters, MM3 is able to reproduce structures (bond lengths and bond angles) and vibrational spectra satisfactorily. © 1994 by John Wiley & Sons, Inc.     

Theoretical studies of uracil–(H2O)n (n = 1–7) clusters by ab initio and ABEEMσπ/MM fluctuating charge model

Uracil–(H₂O)_n (n = 1–7) clusters were systemically investigated by ab initio methods and the newly constructed ABEEMσπ/MM fluctuating charge model. Water molecules have been gradually placed in an average plane containing uracil. The geometries of 38 uracil–water complexes were obtained using B3LYP/6-311++G** level optimizations, and the energies were determined at the MP2/6-311++G** level with BSSE corrections. The ABEEMσπ/MM potential model gives reasonable properties of these clusters when comparing with the present ab initio data. For interaction energies, the root mean square deviation is 0.96 kcal/mol, and the linear coefficient reaches 0.997. Furthermore, the ABEEMσπ charges changed when H₂O interacted with the uracil molecule, especially at the sites where the hydrogen bond form. These results show that the ABEEMσπ/MM model is fine giving the overall characteristic hydration properties of uracil–water systems in good agreement with the high-level ab initio calculations.     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

Force field for computation of conformational energies,structures, and vibrational frequencies of aromatic polyesters

A CFF93¹ all-atom force field for aromatic polyesters based on ab initio calculations is reported. The force field parameters are derived by fitting to quantum mechanical data which include total energies, first and second derivatives of the total energies, and electrostatic potentials. The valence parameters and the ab initio electrostatic potential (ESP) derived charges are then scaled to correct the systematic errors originating from the truncation of the basis functions and the neglect of electron correlation in the HF/6-31G* calculations. Based on the force field, molecular mechanics calculations are performed for homologues of poly(p-hydroxybenzoic acid) (PHBA) and poly(ethylene terephthalate) (PET). The force field results are compared with available experimental data and the ab initio results. © 1994 by John Wiley & Sons, Inc.     

Chlorosilanes: Development and application of MM2 force field parameters

The geometries, relative conformational energies, and dipole moments of mono and polychlorosilanes have been calculated using ab initio molecular orbital (MO) theory. Calculations at the HF/3–21G(*) level, with the exception of dipole moments, give reasonable agreement with experimental data. A new MM2 force field for chlorosilanes, which includes terms for bond length shortening and bond angle compression due to the attachment of electronegative Cl atoms, has been developed on the basis of experimental and ab initio results. The new force field is generally successful in predicting structural parameters, but is unable to reproduce the dipole moments of several model systems. While dipole moment predictions are not the authors' main interest, this failure defines a shortcoming in the MM2 method. The new parameters have been applied to problems in the prediction of stereochemistries of cyclic systems, and compared with experimental results where data are available.     

Combined molecular mechanical and quantum mechanical potential study of a nucleophilic addition reaction in solution

The procedure of combined semiempirical quantum mechanical (AM1) and molecular mechanical potential⁷ was used to study the nucleophilic addition of hydroxide to formaldehyde in solution. The gas phase AM1 potential surface is approximately 26 kcal/mol more exothermic than the corresponding ab initio 6-31 + G* calculation results. The free energy profile for the reaction in solution was determined by means of molecular dynamic simulations. The resulting free energy of activation is approximately 5 kcal/mol. The difference of the free energy of solvation between the reactant and the product states is about 38 kcal/mol. As the reaction goes on, the number of hydrogen bonds formed by the hydroxide oxygen with the surrounding water molecules decreases, whereas the number of hydrogen bonds formed by the carbonyl oxygen increases. There is no significant change in the total number of hydrogen bonds between the solute and the solvent molecules, and the average number of these hydrogen bonds is between five and six during the entire reaction process. These results are consistent with previous studies using a model based on ad initio 6-31 + G* calculations in the gas phase. The reaction path in solution is different from the gas phase minimum energy reaction path. When the two reactants are at a large distance, the attack route of the hydroxide anion in solution is close to perpendicular to the formaldehyde plane, whereas in the gas phase the route is collinear with the carbonyl group. These results suggests that although AM1 does not yield accurate energies in the gas phase, valuable insights into the solvent effects can be obtained through computer simulations with this combined potential. This combined procedure could be applied to chemical reactions within macromolecules, in which a quantitative estimation of the effects of the environment would not be easily attainable by another technique. © 1994 by John Wiley & Sons, Inc.     

Ab initio and molecular mechanics calculations on imine derivatives: A study of the rotational barriers and the development of MM2 parameters

The application of molecular mechanics methods for the study of structures has become a standard approach to conformational analysis. The MM2 force field has been extended to include imines. In general, a diverse group of aliphatic and aromatic imine structures can now be treated. The rotational energy profiles and barriers to N-substituted imines about the C_sp2? C_sp2 single bonds adjacent to C?N functional group were calculated via ab initio MO theory. Information obtained from the quantum mechanical calculations at the 3-21G, 6-31G*, and MP4/6-31G* //6-31G* levels was used both to study the phenomena involved and to parameterize MM2. The syn-anti isomerization was also studied, and the mechanistic pathways have been evaluated. In cases where the comparison with experimental data can be made, the agreements are good.     

Accurate modeling of the intramolecular electrostatic energy of proteins

The (?, ψ) energy surface of blocked alanine (N-acetyl–N′-methyl alanineamide) was calculated at the Hartree-Fock (HF)/6-31G* level using ab initio molecular orbital theory. A collection of six electrostatic models was constructed, and the term electrostatic model was used to refer to (1) a set of atomic charge densities, each unable to deform with conformation; and (2) a rule for estimating the electrostatic interaction energy between a pair of atomic charge densities. In addition to two partial charge and three multipole electrostatic models, this collection includes one extremely detailed model, which we refer to as nonspherical CPK. For each of these six electrostatic models, parameters—in the form of partial charges, atomic multipoles, or generalized atomic densities—were calculated from the HF/6-31G* wave functions whose energies define the ab initio energy surface. This calculation of parameters was complicated by a problem that was found to originate from the locking in of a set of atomic charge densities, each of which contains a small polarization-induced deformation from its idealized unpolarized state. It was observed that the collective contribution of these small polarization-induced deformations to electrostatic energy differences between conformations can become large relative to ab initio energy differences between conformations. For each of the six electrostatic models, this contribution was reduced by an averaging of atomic charge densities (or electrostatic energy surfaces) over a large collection of conformations. The ab initio energy surface was used as a target with respect to which relative accuracies were determined for the six electrostatic models. A collection of 42 more complete molecular mechanics models was created by combining each of our six electrostatic models with a collection of seven models of repulsion + dispersion + intrinsic torsional energy, chosen to provide a representative sample of functional forms and parameter sets. A measure of distance was defined between model and ab initio energy surfaces; and distances were calculated for each of our 42 molecular mechanics models. For most of our 12 standard molecular mechanics models, the average error between model and ab initio energy surfaces is greater than 1.5 kcal/mol. This error is decreased by (1) careful treatment of the nonspherical nature of atomic charge densities, and (2) accurate representation of electrostatic interaction energies of types 1—2 and 1—3. This result suggests an electrostatic origin for at least part of the error between standard model and ab initio energy surfaces. Given the range of functional forms that is used by the current generation of protein potential functions, these errors cannot be corrected by compensating for errors in other energy components. © 1995 by John Wiley & Sons, Inc.     

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.     

Molecular electrostatic potentials and partial atomic charges from correlated wave functions: Applications to the electronic ground and excited states of 3-methylindole

Procedures have been developed to generate molecular electrostatic potentials based on correlated wave function from ab initio or semiempirical electronic structure programs. A new algorithm for point-wise sampling of the potential is described and used to obtain partial atomic charges via a linear, least squares fit between classical and quantum mechanical electrostatic potentials. The proposed sampling algorithm is efficient and promises to introduce less rotational variance in the potential derived partial charges than algorithms applied previously. Electrostatic potentials and fitted atomic charges from ab initio (HF/6–31G* and MP2/6-31G*) and semiempirical (INDO/S; HF, SECI, and SDCI) wave functions are presented for the electronic ground (S₀) and excited (¹L_b, ¹L_a) states of 3-methylindole. © 1992 by John Wiley & Sons, Inc.     

Directional hydrogen bonding in the MM3 force field: II

Extensive calculations on hydrogen bonded systems were carried out using the improved MM3 directional hydrogen bond potential. The resulting total function was reoptimized. Comparisons of the hydrogen bonding potential function from ab initio calculations (MP2/6-31G**); the original MM3(89); and the reoptimized MM3 force field MM3(96), for a variety of C, N, O, and Cl systems including the formamide dimer and formamide–water complex, are described herein. Hydrogen bonding is shown to be a far more complicated and ubiquitous phenomenon than is generally recognized. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1001–1016, 1998     

A theoretical study on the structure and properties of phenothiazine derivatives and their radical cations

Semiempirical CNDO, AM1, PM3 and ab initio HF/STO-3G, HF/3-21G(d), and HF/6-31(d) methods were employed in the geometry optimization of the phenothiazine and the corresponding radical cation. The results obtained from the PM3 performances were as good as those from the ab initio calculations in the structure optimization of both phenothiazine and phenothiazine radical cation. The PM3 method was used to optimize the structures of a series of N-substituted phenothiazine derivatives and their radical cations. The PM3-optimized results were then analyzed with the ab initio calculation at the 6-311G(d,p) level, which yielded the total energy, frontier molecular orbitals, dipole moments, and charge and spin density distributions of the phenothiazine derivatives and their radical cations.     

Quantum supercharger library: Hyper‐parallel integral derivatives algorithms for ab initio QM/MM dynamics

This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two‐electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one‐ and two‐electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree–Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS‐UK, which uses the efficient Schlegel method for ‐ and ‐orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6‐31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc.     

Conformational preferences for hydroxyl groups in substituted tetrahydropyrans

Quantum mechanical (ab initio and semiempirical) and force field calculations are reported for representative torsion potentials in several tetrahydropyran derivatives. The overall agreement between the various methods is quite good except that the AMBER torsion profiles are sensitive to the choice of atomic point charges. Using electrostatic potential (ESP) derived atomic point charges determined with the STO-3G basis set we find that AMBER is able to match the best quantum mechanical results quite well. However, when the point charges are derived using the 6-31G* basis set we find that scaling the intramolecular electrostatic nonbond interactions is necessary. AM1 does not work very well for these compounds when compared to the ab initio methods and, therefore, should only be used in cases when ab initio calculations would be prohibitive. Based upon our results we feel that any force field that makes use of 6-31G* ESP derived atomic point charges will need to scale intramolecular interactions. Implications of scaling intramolecular interactions to the development of force fields based on 6-31G* ESP derived atomic point charges are discussed. © 1992 by John Wiley & Sons, Inc.     

Simulations of internal rotation potential energies for substituted ethanes

Two approaches to the simulation of internal rotation potential energies in substituted ethanes are formulated for general applications. Called the vicinal Fourier coefficient and vicinal pair energy methods, they differ only in form. The latter procedure has the advantage of yielding energy terms that represent pairwise interactions between vicinal substitutents. As numerical examples, the potential energies of ethane and five of its simple methyl and chloro derivatives are employed to simulate the corresponding energies of two higher derivatives of the series. The initial energy data were calculated by the molecular mechanics method (MM2) with geometry optimizations and the ab initio MO procedure (STO-3G) with standard geometries. Results indicate that simulated energies are reasonably accurate for the flexible-rotor model (MM2) and extremely accurate for the rigid-rotor model (STO-3G). Deviations appear to be systematic and may be rationalized on the basis of molecular structure.