Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part II. Accurate energy minimization

A method is described to perform ab initio energy minimization for crystals of flexible molecules. The intramolecular energies and forces are obtained directly from ab initio calculations, whereas the intermolecular contributions follow from a potential that had been parameterized earlier on highly accurate quantum‐chemical calculations. Glycol and glycerol were studied exhaustively as prototypes. Lists of hypothetical crystal structures were generated using an empirical force field, after which ab initio energy minimizations were performed for a few hundreds of these. The experimental crystal structures were found among the structures with lowest energy, provided that sufficiently large basis sets were used. Moreover, their crystal geometries were well reproduced. This approach enables a systematic comparison between the merits of force fields at various levels of sophistication. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 805–815, 2001     

Protein structure prediction using a combination of sequence homology and global energy minimization: II. Energy functions

A protein energy surface is constructed. Validation is through applications of global energy minimization to surface loops of protein crystal structures. For 9 of 10 predictions, the native backbone conformation is identified correctly. Electrostatic energy is modeled as a pairwise sum of interactions between anisotropic atomic charge densities. Model repulsion energy has a softness similar to that seen in ab initio data. Intrinsic torsional energy is modeled as a sum over pairs of adjacent torsion angles of 2-dimensional Fourier series. Hydrophobic energy is that of a hydration shell model. The remainder of hydration free energy is obtained as the energetic effect of a continuous dielectric medium. Parameters are adjusted to reproduce the following data: a complete set of ab initio energy surfaces, meaning one for each pair of adjacent torsion angles of each blocked amino acid; experimental crystal structures and sublimation energies for nine model compounds; ab initio energies over 1014 conformations of 15 small-molecule dimers; and experimental hydration free energies for 48 model compounds. All ab initio data is at the Hartree–Fock/6–31G* level. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 548–573, 1998     

Base stacking in cytosine dimer. A comparison of correlated ab initio calculations with three empirical potential models and density functional theory calculations

Ab initio MP2/6-31G* interaction energies were calculated for more than 80 geometries of stacked cytosine dimer. Diffuse polarization functions were used to properly cover the dispersion energy. The results of ab initio calculations were compared with those obtained from three electrostatic empirical potential models, constructed as the sum of a Lennard-Jones potential (covering dispersion and repulsion contributions) and the electrostatic term. Point charges and point multipoles of the electrostatic term were also obtained at the MP2/6-31G* level of theory. The point charge MEP model (atomic charges derived from molecular electrostatic potential) satisfactorily reproduced the ab initio data. Addition of π-charges localized below and above the cytosine plane did not affect the calculated energies. The model employing the distributed multipole analysis gave worse agreement with the ab initio data than the MEP approach. The MP2 MEP charges were also derived using larger sets of atomic orbitals: cc-pVDZ, 6-311 + G(2d, p), and aug-cc-pVDZ. Differences between interaction energies calculated using these three sets of point charges and the MP2/6-31G* charges were smaller than 0.8 kcal/mol. The correlated ab initio calculations were also compared with the density functional theory (DFT) method. DFT calculations well reproduced the electrostatic part of interaction energy. They also covered some nonelectrostatic short-range effects which were not reproduced by the empirical potentials. The DFT method does not include the dispersion energy. This energy, approximated by an empirical term, was therefore added to the DFT interaction energy. The resulting interaction energy exhibited an artifact secondary minimum for a 3.9-4.0 vertical separation of bases. This defect is inherent in the DFT functionals, because it is not observed for the Hartree-Fock + dispersion interaction energy.© 1996 John Wiley & Sons, Inc.     

Quantum chemical prediction of the adsorption conformations and dynamics at HCOOH‐covered ZnO(1010) surfaces

Results from ab initio Hartree–Fock and gradient‐corrected density functional theory calculations of formic acid interactions with ZnO (101 0) surfaces are reported. Surface relaxation is found to affect equilibrium geometries and adsorption energies significantly. Large variations in adsorption energy with coverage and ordering of the adsorbates are revealed and explained in terms of strong and highly anisotropic electrostatic adsorbate–adsorbate interactions. The results are compared to published experimental and theoretical results, and differences in suggested binding geometries from the different studies are discussed. Dynamic properties of the adsorption, surface mobility, and surface reactivity are inferred from key elements of the potential energy surface obtained from the quantum chemical computations and supported by ab initio molecular dynamics simulations. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Comparison of ab initio,semiempirical, and molecular mechanics calculations for the conformational analysis of ring systems

The potential energy surfaces of four cyclic alkanes have been examined using molecular mechanics, semiempirical, and ab initio methods to determine if they produce mutually consistent results and investigate the source of any errors between the methods. The C₅ ? C₈ cyclic alkanes were chosen since these structures present a finite set of conformations and transition-state geometries and are still within the computational time and memory limits of the quantum mechanical approaches. We also examined several conformations of 1,2-dideoxyribose to determine the effect of heteroatoms on the results for the 5-membered ring. The molecular mechanics and ab initio calculations are consistent in the relative energies and geometries determined for the conformers of all ring systems. While the semiempirical calculations yielded geometries consistent with the other methods (except for 5-membered rings), the relative energies often deviated substantially. A decomposition analysis of the semiempirical and molecular mechanics energies revealed that the disparities are mainly due to errors in the 1-center energies of the semiempirical calculations. The 2-center bonding and nonbonding energies followed reasonable trends for the conformers. The core-repulsion function, however, is suspected of producing anomalies. A minimum in the attractive Gaussian of this term at 2.1 Å for H? H interactions partly explains the propensity of the 5-membered rings to optimize to near planarity (decreasing 1,2-diaxial hydrogen distances to 2.3 Å) and the underestimation of the relative energy of the boat structure of cyclohexane.     

A molecular mechanics model for imatinib and imatinib:kinase binding

Imatinib is an important anticancer drug, which binds specifically to the Abl kinase and blocks its signalling activity. To model imatinib:protein interactions, we have developed a molecular mechanics force field for imatinib and four close analogues, which is consistent with the CHARMM force field for proteins and nucleic acids. Atomic charges and Lennard‐Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with imatinib fragments at 32 different positions. We considered both a neutral and a protonated imatinib. The final RMS deviation between the ab initio and force field energies, averaged over both forms, was 0.2 kcal/mol. The model also reproduces the ab initio geometry and flexibility of imatinib. To apply the force field to imatinib:Abl simulations, it is also necessary to determine the most likely imatinib protonation state when it binds to Abl. This was done using molecular dynamics free energy simulations, where imatinib is reversibly protonated during a series of MD simulations, both in solution and in complex with Abl. The simulations indicate that imatinib binds to Abl in its protonated, positively‐charged form. To help test the force field and the protonation prediction, we did MD free energy simulations that compare the Abl binding affinities of two imatinib analogs, obtaining good agreement with experiment. Finally, two new imatinib variants were considered, one of which is predicted to have improved Abl binding. This variant could be of interest as a potential drug. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A CNDO/INDO molecular orbital formalism for the elements H to Br. applications

The CNDO/INDO molecular orbital formalism introduced in the preceding paper has been applied to a large number of atom combinations up to bromine under the inclusion of the first transition metal series. The results are compared with experimental data (geometries, ionization potentials, dipole moments) or with the results of sophisticatedab initio calculations (one electron energies, net charges, atomic populations). The semiempirical model reproduces for a wide range of molecules the experimental andab initio data with remarkable success.     

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     

Theoretical studies on ammonia oxide and its unimolecular reactions

The unimolecular reactions of ammonia oxide H₃NO, isomerization and dehydrogenation, are investigated by ab initio MO calculations with the 4-31G basis set. The geometries and energies of the reactant, transition states and products have been determined on the singlet potential energy surface. The reaction ergodography along the intrinsic reaction coordinate (IRC) for the two reactions have been performed. The vibrational frequency correlation diagram of the two reactions are analyzed along the IRC.     

Studies in hydrogen bonding: Association within mixed dimers of water,methanol, ammonia,and methylamine using the empirical potential EPEN

An empirical potential EPEN has been used to find the stable geometries and approximate hydrogenbond energies of the mixed dimers formed between molecules of water, methanol, ammonia, and methylamine. These results are compared with results in the literature obtained using ab initio methods.     

Systematic errors in the total energy of molecular wave functions calculated within the PRDDO approximations

We compare calculated total energies for 150 open-chain molecules using ab initio methodology and the PRDDO approximations. The bulk of the errors implicit in the PRDDO approximations are apparently of a one-center nature, i.e., they are due to the number and type of atoms in the molecule, and not the details of the molecular geometry. Atomic correction factors are developed which reduce the errors in the calculated total energy of PRDDO wave functions by a factor of eight relative to the ab initio reference calculations. PRDDO calculations on ring and cage compounds are shown to have additional systematic errors in the total energy.     

Parallel ab initio and molecular mechanics investigation of polycoordinated Zn(II) complexes with model hard and soft ligands: Variations of binding energy and of its components with number and charges of ligands

In this study we compare the binding energies of polycoordinated complexes of Zn²⁺ within cavities composed of model “hard” (H₂O, OH⁻) or “soft” (CH₃SH, CH₃S⁻) ligands. Ab initio supermolecule computations are performed at the HF and MP2 levels using extended basis sets to determine the binding energies and their components as a function of: the number of ligands, ranging from three to six; the net charge of the cavity; and the “hard” versus “soft” character of the ligands. These ab initio computations are used to test the reliability of the SIBFA molecular mechanics procedure, originally formulated and calibrated on the basis of ab initio computations, for such charged systems. The SIBFA intermolecular interaction energies match the corresponding ab initio values using a coreless effective potential split‐valence basis set with a relative error of ≤3%. Extensions to binuclear Zn²⁺ complexes, such as those that occur in the Zn‐binding sites of Gal4 and β‐lactamase proteins, are performed to test the applicability of the methodology for such systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1011–1039, 2000     

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.     

Potential energy function for cation–peptide interactions: An ab initio study

A potential energy function is developed to represent the interaction of small monovalent cations, Li⁺, Na⁺, and K⁺, with the backbone of polypeptides. The results are based on ab initio calculations up to the 6-31G* level of the interactions of the ions with acetamide and N-methylacetamide. Basis set superposition errors are corrected with the counterpoise method. A systematic overestimate of the bond polarities is taken into account by an empirical scaling procedure that uses the ratio of the experimental to ab initio dipole moment. The calculated binding energies obtained with this procedure show consistent convergence with different basis sets and are in good agreement with experimental data on cation–water and cation–dimethylformamide systems. Investigations of the calculated ab initio potential energy surface indicate that the cation–peptide interaction is dominated by electrostatics and includes a nonnegligible contribution from polarization of the peptide group by the ion. The induced polarization results in a steeper-than-Coulombic interaction and cannot be described by fixed ion–peptide partial charges electrostatics. Atomic polarizabilities located on the atoms of the ligand molecule are introduced to account for the induced polarization in the empirical energy function. A ～1/r⁴ attractive interaction appears in the potential function. The resulting radial and angular dependence of the potential energy surface is well reproduced. © 1995 by John Wiley & Sons, Inc.     

Effective way of modeling chemical catalysis: Empirical valence bond picture of role of solvent and catalyst in alkylation reactions

A general methodology for the study of chemical catalysis is presented and demonstrated in a study of Friedel–Crafts‐type alkylation reactions that are constrained to collinear configurations. Ab initio potential energy surfaces in solution and relevant experimental results are used to calibrate general empirical valence bond (EVB) potential surfaces for studies of such reactions. The EVB surfaces allow one to interpolate the ab initio results to studies of the effect of different solvents, substituents, and catalysts on the alkylation reactions. This implicit approach introduces such effects by shifting the diagonal energies of the corresponding resonance structures. Such an EVB/shift approach appears valuable for assessing the effects of different catalysts and solvents on complex chemical reactions. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 607–625, 2000     

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.     

A systematic preparation of new contracted Gaussian-type orbital sets. VI. Ab initio calculation on molecules containing Na through Cl

Compact contracted Gaussian basis sets introduced in the preceding article are tested for ab initio molecular calculations on molecules containing third-row atoms (Na through Cl). It is found that the effect of splitting valence orbitals is essential for these molecules and addition of polarization functions to split basis sets can yield computed geometries, spectroscopic constants, and atomization energies in close agreement with the result of near Hartree–Fock calculations.     

Analysis of the core-repulsion functions used in AM1 and PM3 semiempirical calculations: Conformational analysis of ring systems

The AM1 and PM3 potential energy surfaces of cyclopentane have been compared and the energy difference between two (boat and chair) cyclohexane conformers analyzed. The effects of reparameterization and different core-repulsion functions (CRFs) have been studied. The H? H, C? H, and C? C CRF energy contributions have been calculated separately. The results show that the CRF energy corrections stabilize the correct (MM2 and ab initio) geometries. The PM3 equilibrium geometry of cyclopentane is closer to the MM2 and ab initio results than the AM1 geometry. It is known that above 190 pm the AM1 H? H CRF curve is smooth and negative but the PM3 H? H CRF curve has a trough and a shoulder. It has been shown that this latter oscillation is not damped by other parameters. As a result, the H? H PM3 energy gradient curve is different from the quasilinear AM1 and ab initio gradient curves. © 1993 John Wiley & Sons, Inc.