Global Minimum Energy Structure Research Articles

Energy-directed tree search: an efficient systematic algorithm for finding the lowest energy conformation of molecules

We present a new systematic algorithm, energy-directed tree search (EDTS), for exploring the conformational space of molecules. The algorithm has been designed to reliably locate the global minimum (or, in the worst case, a structure within 4 kJ mol(-1) of this species) at a fraction of the cost of a full conformational search, and in this way extend the range of chemical systems for which accurate thermochemistry can be studied. The algorithm is inspired by the build-up approach but is performed on the original molecule as a whole, and objectively determines the combinations of torsional angles to optimise using a learning process. The algorithm was tested for a set of 22 large molecules, including open- and closed-shell species, stable structures and transition structures, and neutral and charged species, incorporating a range of functional groups (such as phenyl rings, esters, thioesters and phosphines), and covering polymers, peptides, drugs, and natural products. For most of the species studied the global minimum energy structure was obtained; for the rest the EDTS algorithm found conformations whose total electronic energies are within chemical accuracy from the true global minima. When the conformational space is searched at a resolution of 120 degrees , the cost of the EDTS algorithm (in its worst-case scenario) scales as 2(N) for large N (where N is the number of rotatable bonds), compared with 3(N) for the corresponding systematic search.

Ab initio study of XenI− (n = 1–6) clusters

The structures, stabilities and electron affinities of XenI− (n=1–6) clusters were studied at MP2 theoretical level. In the global minimum energy structures, all the Xe atoms contact the central iodine anion. The electron correlation effects on the geometry and stability is investigated and it stabilizes title clusters. The calculated electron affinities are in good agreement with the experimental results. The Xe6I− has the biggest fragmentation energy and thus it is the most stable species.

Analyzing energy landscapes for folding model proteins

A new benchmark 20-bead HP model protein sequence (on a square lattice), which has 17 distinct but degenerate global minimum (GM) energy structures, has been studied using a genetic algorithm (GA). The relative probabilities of finding particular GM conformations are determined and related to the theoretical probability of generating these structures using a recoil growth constructor operator. It is found that for longer successful GA runs, the GM probability distribution is generally very different from the constructor probability, as other GA operators have had time to overcome any initial bias in the originally generated population of structures. Structural and metric relationships (e.g., Hamming distances) between the 17 distinct GM are investigated and used, in conjunction with data on the connectivities of the GM and the pathways that link them, to explain the GM probability distributions obtained by the GA. A comparison is made of searches where the sequence is defined in the normal (forward) and reverse directions. The ease of finding mirror image solutions are also compared. Finally, this approach is applied to rationalize the ease or difficulty of finding the GM for a number of standard benchmark HP sequences on the square lattice. It is shown that the relative probabilities of finding particular members of a set of degenerate global minima depend critically on the topography of the energy landscape in the vicinity of the GM, the connections and distances between the GM, and the nature of the operators used in the chosen search method.

Determination of the Preferred Conformation of the Bicyclic Galerucella Pheromone Using Density Functional Theory Optimization and Calculations of Chemical Shifts

A pheromone from the beetle, Galerucella calmariensis, was recently isolated and identified (Bartelt, R. J. et al. J. Chem. Ecol. 2006, 32, 693-712) as a 14-carbon, bicyclic dimethylfuran lactone, with the systematic name 12,13-dimethyl-5,14-dioxabicyclo[9.2.1]tetradeca-1(13),11-dien-4-one. The main 12-membered lactone ring is very flexible; as a result, there exist multiple possible conformations. The preferred conformation cannot be deduced solely from room-temperature NMR measurements. Using density functional (DFT) studies, 26 unique conformers with energies within 10.0 kcal/mol of the global minimum-energy structure were found. A mirror-image plane exists so that each conformer has an "inverse" structure with the same energy, for which the dihedral angles around the flexible ring have opposite sign. The isotropic 1H and 13C NMR chemical shifts of the DFT-optimized structures were calculated using the gauge-including atomic orbital (GIAO) method. By considering the relative energies of the conformers and the calculated and observed NMR spectra, we concluded that the molecule exists primarily as a mixture of two distinct conformers at room temperature, each being present with its mirror-image inverse. Structural interconversions among these likely occur on a time scale that is fast compared to the NMR experiments. Using mode-following and dihedral-driving techniques, several potential pathways were found for the conversion of the lowest-energy conformer to its mirror-image structure. Ab initio molecular dynamics (AIMD) using the 4-31G basis set was carried out for 50 ps to test the availability of various low-energy minima and the transition states found from the searches noted above.

Larger Water Clusters with Edges and Corners on Their Way to Ice: Structural Trends Elucidated with an Improved Parallel Evolutionary Algorithm

For the difficult task of finding global minimum energy structures for molecular clusters of nontrivial size, we present a highly efficient parallel implementation of an evolutionary algorithm. By completely abandoning the traditional concept of generations and by replacing it with a less rigid pool concept, we have managed to eliminate serial bottlenecks completely and can operate the algorithm efficiently on an arbitrary number of parallel processes. Nevertheless, our new algorithm still realizes all of the main features of our old, successful implementation. First tests of the new algorithm are shown for the highly demanding problem of water clusters modeled by a potential with flexible, polarizable monomers (TTM2-F). For this problem, our new algorithm not only reproduces all of the global minima proposed previously in considerably less CPU time but also leads to improved proposals in several cases. These, in turn, qualitatively change our earlier predictions concerning the transitions from all-surface structures to cages with a single interior molecule, and from one to two interior molecules. Furthermore, we compare preliminary results up to n = 105 with locally optimized cuts from several ice modifications. This comparison indicates that relaxed ice structures may start to be competitive already at cluster sizes above n = 90.

Ab initio study of hydrated sodium halides NaX(H2O)1–6 (X=F, Cl, Br, and I)

We have studied the dissociation phenomena of sodium halides by water molecules. The structures, binding energies, electronic properties, and IR spectroscopic features have been investigated by using the density-functional theory, second-order Moller-Plesset perturbation theory, and coupled clusters theory with single, double, and perturbative triplet excitations. In the case that the sodium halides are hydrated by three water molecules, the most stable structures show the partial (or half) dissociation feature. The dissociated structures are first found for NaX(H2O)(n=5) for X=BrI, though these structures are slightly higher in energy than the global minimum-energy structure. In the case of hexahydrated sodium halides the global minimum-energy structures (which are different from the structures reported in any previous work) are found to be dissociated (X=F/I) or partially/half dissociated (X=Cl/Br), while other nearly isoenergetic structures are undissociated, and the dissociated cubical structures are higher in energy than the corresponding global minimum-energy structure.

The ω, φ, and ψ Space of N-Hydroxy-N-methylacetamide and N-Acetyl-N '-hydroxy-N '-methylamide of Alanine and Their Boron Isosteres.

The conformational space of N-hydroxy-N-methylacetamide [CH3-CO-N(OH)CH3, NMAOH] and its boron isostere [CH3-CO-B(OH)CH3, BMAOH] has been studied by quantum chemical methods. The potential energy surface of NMAOH and BMAOH has been built at the HF, B3LYP, and MP2 levels of theory with the 6-31+G* basis set. The minima and transition states for rotations about various torsional angles have been located, and the energy barriers have been estimated. The global minimum energy structure of both peptides exhibits an intramolecular hydrogen bond between the carbonyl oxygen and the hydroxyl group, imparting a conformational rigidity to the peptides. The omega rotation barrier is lower in the boron isostere than in NMAOH. The difference in the rotation barrier has been attributed to second-order orbital interactions, like negative hyperconjugation, as revealed by NBO calculations. In contrast, the rotation barrier around the torsion angle tau (torsion governing rotation about the N-O and B-O bonds) is relatively higher in the boron analogue. This difference is due to the double bond character in the B-O bond as opposed to the N-O bond which has the character of a single bond. As an extension, N-acetyl-N'-hydroxy-N'-methylamide of alanine (Ala-NOH) and its boron isostere (Ala-BOH) have been adopted as model peptides to study the conformational preferences about the φ and ψ torsion angles. The study reveals a strong preference for a Type I beta turn as well as inclinations for a left-handed alpha helix, for positive phi torsions, and for extended psi conformations for Ala-NOH; Ala-BOH, on the other hand, shows a leaning toward positive phi and extended psi, with no preference for any regular secondary structure motifs. The replacement of nitrogen by boron changes the electronic and conformational properties of the peptide, extending greater flexibility around the omega angle, a strong preference for positive phi values, and a shift in the site of nucleophilic attack from the carbonyl group to boron.

Dissolution Nature of Cesium Fluoride by Water Molecules

The structures, stabilities, thermodynamic quantities, dissociation energies, infrared spectra, and electronic properties of CsF hydrated by water molecules are investigated by using density functional theory, Møller-Plesset second-order perturbation theory (MP2), coupled cluster theory with singles, doubles, and perturbative triples excitations (CCSD(T)), and ab initio molecular dynamic (AIMD) simulations. It is revealed that at 0 K three water molecules (as a global minimum structure) begin to half-dissociate the Cs-F, and six water molecules (though not a global minimum energy structure) can dissociate it. By the combination of the accurate CCSD(T) conformational energies for Cs(H2O)6 at 0 K with the AIMD thermal energy contribution, it reveals that the half-dissociated structure is the most stable at 0 K, but this structure (which is still the most stable) changes to the dissociated structure above 50 K. The spectra of CsF(H2O)(1-6) from MP2 calculations and the power spectra of CsF(H2O)6 from 50 and 100 K AIMD simulations are also reported.

Melting in small gold clusters: a density functional molecular dynamics study

Molecular dynamics simulations of the thermal behaviour of gold clusters containing 7, 13and 20 atoms have been performed. Total energies and forces at each step of thesimulation are calculated from first principles using density functional theory. Iontrajectories are then calculated classically from these forces. In each case the globalminimum energy structure and a low-lying isomer are used as the starting structures.In most cases, the clusters do not exhibit a sharp transition from a solid-likephase to a liquid-like phase, but rather pass through a region of transformationsbetween structural isomers that extends over a considerable temperature range.Solid-like behaviour is observed in the atomic trajectories of the simulation attemperatures up to, or above, the bulk melting point. The 20-atom tetrahedralstructure is the one exception, showing a sharp transition between solid-like andliquid-like phases at about 1200 K. The starting structure used in the simulationis shown to have a considerable effect upon the subsequent thermal behaviour.

AMBER force field implementation of the boronate function to simulate the inhibition of β-lactamases by alkyl and aryl boronic acids

Boronic acids are a very appealing class of serine proteases inhibitors whose rational design suffers, in spite of their therapeutic potential, from the lack of boron-related parameters in force fields commonly used for proteins. We introduced bonded, non-bonded and point charges in the MacroModel/Amber force field, as well as GB/SA solvation parameters, to model boronic acids as tetrahedral adducts formed after protease’s serine Oγ coordination. With the aim to check the implemented force field, flexible docking studies were performed on three crystallographic complexes of β-lactamases with boronic acids that output the crystallographic conformation of the complexes as the global minimum energy structure. Although the used approach was basic, nevertheless the resultant force field seems to be efficient and suitable for the structure-based design of new boronic inhibitors of β-lactamases.

CH5+: Chemistry's Chameleon Unmasked

The nuclear vibrational wave function and zero-point vibrational energy of CH5(+) are calculated using quantum diffusion Monte Carlo techniques on an interpolated potential energy surface constructed from CCSD(T)/aug'-cc-pVTZ ab initio data. From this multidimensional wave function, the vibrationally averaged rotational constants and radial distribution functions for atom-atom distances within the molecule are constructed. It is found that the distributions of all 10 H-H distances are bimodal and identical. The radial distribution functions obtained for the five C-H distances are also identical, but unimodal. The three rotational constants were found to be 3.78, 3.80, and 3.83 cm(-1). These values indicate that the ground state of CH5(+) is significantly more symmetric than its global minimum energy structure. We conclude that the zero-point motion of CH5(+) renders all five protons equivalent in the ground state and precludes the assignment of a unique structure to the molecule.

Beyond the Isotropic Atom Model in Crystal Structure Prediction of Rigid Molecules: Atomic Multipoles versus Point Charges

The lattice energies of predicted and known crystal structures for 50 small organic molecules with constrained (rigid) geometries have been calculated with a model potential whose electrostatic component is described by atom-centered multipoles. In comparison to previous predictions using atomic point charge electrostatics, there are important improvements in the reliability of lattice energy minimization for the prediction of crystal structures. Half of the experimentally observed crystal structures are found either to be the global minimum energy structure or to have calculated lattice energies within 0.5 kJ/mol (0.1 kcal/mol) of the global minimum. Furthermore, in 69% of cases, there are five or fewer unobserved structures with lattice energies calculated to be lower than that of the observed structure. The results are promising for the advancement of global lattice energy minimization for the ab initio prediction of crystal structures and confirm the utility of representing electrostatic contributions to the energy with atom-centered multipoles.

Toward Crystal Structure Prediction for Conformationally Flexible Molecules: The Headaches Illustrated by Aspirin

A crystal structure prediction study was carried out on aspirin, based on an analysis of its gas phase conformers and multiple searches for minima in the lattice energy with the molecule held rigid in low energy conformations. Various high levels of ab initio theory were used to estimate the gas phase conformations and energy differences, and accurate distributed multipole-based electrostatic models were used to estimate the electrostatic contribution to the lattice energies. The molecular conformation adopted in the crystal structure is close to a local minimum found in the gas phase ab initio energy using a B3LYP/6-31G(d,p) calculation. A MP2 optimization gives larger differences from the solid state molecular structure. The calculation using the B3LYP molecular conformer predicts the observed crystal structure as one of the most thermodynamically stable and generally the most plausible crystal structure. Alternative molecular conformers, including the gas phase global minimum energy structure and plana...

An Assessment of Lattice Energy Minimization for the Prediction of Molecular Organic Crystal Structures

Lattice energy searches for theoretical low-energy crystal forms are presented for 50 small organic molecules, and we compare the experimentally observed crystal forms to these lists of hypothetical polymorphs. For each known crystal, the relative stability is calculated with respect to the global minimum energy structure, and we determine the number of unobserved structures lower in energy than the experimental form. The distributions of these relative energies and their rankings in the predicted lists are used to determine the efficacy of lattice energy minimization in crystal structure prediction. Although a simple form for the interaction energies has been used, the calculations produce almost a third of the known crystals as the global minimum in energy, and approximately a half of the known structures are within 1 kJ/mol of the global minimum. Molecules with no hydrogen-bonding capacity are most likely to be found close to the global minimum in lattice energy, while increasing the number of possible...

Geometry Optimization of Ba2+(H2O)n Clusters Using a Fast Hybrid Global Optimization Algorithm

AbstractA global optimization called fast hybrid global optimization algorithm was proposed based on genetic algorithm, fast simulated algorithm and conjugated gradient algorithm. We employ it to search the global minimum energy structures of Ba2+(H2O)n clusters for n = 1–30 within the TIP4P model. The results show that Ba2+(H2O)n clusters have the n+0 structure while n = 1–8. When n is in the range 9 ≤ n ≤ 18, the number of water molecules in the first shell around the barium ion is 8 and the other water molecules arrange in the outer shell. In the global minimum structure of Ba2+(H2O)19, the number of the first shell water molecules adds up to 9, and the value is kept until n = 30. According to the computational results, a conclusion that hydration numbers for Ba2+ is 9 can be drawn, which is in agreement with the result by a Monte Carlo simulation.

Energy Landscape of Met-Enkephalin and Leu-Enkephalin Drawn Using Mutually Orthogonal Latin Squares Sampling

Mapping the energy surface is an important step in understanding the protein folding process. However, it requires identification of all stationary points of the system, or at least a large number of them. Locating the full set of stationary points even for Met-enkephalin is intractable by normal sampling procedures that have been proposed to search the energy surface. We have recently suggested an enhanced combinatorial sampling technique that uses mutually orthogonal Latin squares to quickly identify the complete set of low potential energy structures of a molecule. In this paper, we have used this technique to identify 1500 low potential energy structures each for Met-enkephalin and Leu-enkephalin. We have then used a clustering procedure to reduce the sample to a set of unique conformations. Some of these have been identified earlier by other computational simulations as global energy minimum structures. Others structures in the unique set have been observed in experiments, specifically X-ray crystallography. We have used the unique sets to visualize the entire potential energy landscape as two-dimensional projections and as minimum energy envelopes. The potential energy surfaces of these peptides resemble a funnel that is broader, as well as possessing a larger number of minima that are more widely separated, than the picture demonstrated generally in the past. We are able to locate the theoretical and experimental structures on this landscape. In addition, we are able to identify a set of structures that may represent intermediate steps on the folding pathway of these two peptides.

THE ϕ, ψ SPACE OF BORON ISOSTERES OF AMINO ACIDS: ANAB INITIOSTUDY

Boron isosteres [ CH3- CO - BH - CH(R) - CONHCH3; R = CH3, CH2OH , CH2SH ] of natural amino acids have been designed as inhibitors of serine protease based on boron's ability to mimic the transition state of the normal enzyme catalyzed reaction. The conformation and electronic properties of these isosteres have been determined by ab initio calculations at the HF/6-31G** level of theory. The global minimum energy structures of the boron isosteres (which are all identical) and the natural amino acids are radically different. Interestingly, the boron isosteres have favorable conformations with positive values for the ϕ dihedral, which are "disallowed states" for the natural amino acids. This is possible because of the smaller atomic size of boron compared to nitrogen. The molecular electrostatic potential of the boron isosteres is also very different from the natural amino acids. There is a positive potential around the boron atom, which provokes the attack of the Ser195– OH group in the enzyme, resulting in formation of an irreversible enzyme-inhibitor adduct.

A Kr−BrH Global Minimum Structure Determined on the Basis of Potential Morphing

The ν 1 , ν 1 + ν 2 1, and ν 1 + 2ν 2 0 rovibrational spectra of 8 4 Kr:H 7 9 Br and 8 4 Kr:H 8 1 Br are reported using highfrequency wavelength modulation near-infrared diode-laser continuous-wave (cw) supersonic-jet spectroscopy. This information has been combined with previously recorded results from a ground-state microwave analysis and used to determine a scaled and shifted morphed potential that is based on the transformation of an ab initio potential in a nonlinear least-squares fit to the available experimental data. The morphed potential is consistent with a collinear Kr-BrH global minimum structure with R c m = 3.88 A that is 23 ′ 3 cm - 1 more stable than the minimum associated with the collinear Kr-HBr isomeric form, which has R c m = 4.27 A. Thus, the Kr:HBr system has a ground-vibrational-state isomeric structure that differs from the global minimum energy structure, a result that is similar to that found in the Ar:HBr dimer.

Structure and Hydrogen Bonding of Different Isomers of 2-Aminopyridine·NH3 Studied by IR/R2PI Spectroscopy

The electronic and vibrational spectra of the 1:1 clusters of 2-aminopyridine (2AP) with ammonia have been measured using resonant two-photon ionization (R2PI) and IR/R2PI vibrational spectroscopy. Density functional theory calculations were performed to identify structures and assign the vibrational spectra in the NH stretch region. The two lowest-energy isomers have been identified. In isomer I, which is the global minimum energy structure, ammonia forms a strong H bond with the amino group and a weak one with the aromatic nitrogen. The vibrations of the groups involved in this H bonding exhibit red shifts of 110 cm-1 for the donating amino N−H and of 69 cm-1 for the donating N−H group of ammonia. The degeneracy of the two asymmetrical vibrations of ammonia is removed in the cluster, with the corresponding bands at 3438 and 3406 cm-1. In isomer II ammonia forms an H bond to the N−H group which points away from the aromatic nitrogen. This bond is weaker than the corresponding one in isomer I. The stretch...

Structural optimization of atomic clusters by tabu search in descriptor space

We devised a new algorithm – tabu search in descriptor space – for searching the global energy minimum structure of atomic clusters. In each cycle, the algorithm generates many cluster structures randomly, transforms them to a standard form by “symmetrization of interatomic distances”, and calculates structural descriptors for each. Clusters are then screened according to a model energy obtained by interpolation in descriptor space, and only a small fraction (10% or less) are retained for energy evaluation. This cycle is repeated many times. In a final step, clusters are sorted by increasing energy and optimized by conjugate gradient. This method requires between 10 and a 100 times fewer energy evaluations than a good genetic algorithm for locating the global minimum of n-atom clusters (n<35) described by a Lennard-Jones potential. It seems a very promising method for global optimization on energy surfaces calculated by first-principles.