A machine learning technique toward generating minimum energy structures of small boron clusters

The search for a global minimum related to molecular electronic structure and chemical bonding has received wide attention based on some theoretical calculations at various levels of theory. Particle swarm optimization (PSO) algorithm and modified PSO have been used to predict the energetically stable/metastable states associated with a given chemical composition. Out of a variety of techniques such as genetic algorithm, basin hopping, simulated annealing, PSO, and so on, PSO is considered to be one of the most suitable methods due to its various advantages over others. We use a swarm‐intelligence based parallel code to improve a PSO algorithm in a multidimensional search space augmented by quantum chemical calculations on gas phase structures at 0 K without any symmetry constraint to obtain an optimal solution. Our currently employed code is interfaced with Gaussian software for single point energy calculations. The code developed here is shown to be efficient. Small population size (small cluster) in the multidimensional space is actually good enough to get better results with low computational cost than the typical larger population. But for larger systems also the analysis is possible. One can try with a large number of particles as well. We have also analyzed how arbitrary and random structures and the local minimum energy structures gravitate toward the target global minimum structure. At the same time, we compare our results with that obtained from other evolutionary techniques.     

From molecule to solid: The prediction of organic crystal structures

A method for predicting the structure of a molecular crystal based on the systematic search for a global potential energy minimum is considered. The method takes into account unequal occurrences of the structural classes of organic crystals and symmetry of the multidimensional configuration space. The programs of global minimization PMC, comparison of crystal structures CRYCOM, and approximation to the distributions of the electrostatic potentials of molecules FitMEP are presented as tools for numerically solving the problem. Examples of predicted structures substantiated experimentally and the experience of author’s participation in international tests of crystal structure prediction organized by the Cambridge Crystallographic Data Center (Cambridge, UK) are considered.     

The symmetrized random matrix approach, an efficient method to obtain relativistic molecular symmetry adapted functions

In relativistic quantum chemical calculation of molecules, where the spin-orbit interaction is included, the electron orbitals possess both the double point group symmetry and the time-reversal symmetry. If symmetry adapted functions are employed as the basis functions of electron orbitals, it would allow a significant reduction of the computational expense. The point group symmetry adapted functions can be obtained by the group projection operators via its actions on the atomic orbital functions. We have proposed an efficient and simple method to obtain all irreducible representation matrices, which are the basis of the group projection operators, of any finite double point group. Both double point group symmetry and time-reversal symmetry are automatically imposed on the representation matrices. This is achieved by the symmetrized random matrix (SRM) approach, where the SRM is constructed in the regular representation space of a finite group and the eigenfunctions of SRM provide all irreducible representation matrices of the given point group.     

Alternative search strategy for minimal energy nanocluster structures: the case of rhodium, palladium, and silver

An alternative strategy to find the minimal energy structure of nanoclusters is presented and implemented. We use it to determine the structure of metallic clusters. It consists in an unbiased search, with a global minimum algorithm: conformational space annealing. First, we find the minima of a many-body phenomenological potential to create a data bank of putative minima. This procedure assures us the generation of a set of cluster configurations of large diversity. Next, the clusters in this data bank are relaxed by ab initio techniques to obtain their energies and geometrical structures. The scheme is successfully applied to magic number 13 atom clusters of rhodium, palladium, and silver. We obtained minimal energy cluster structures not previously reported, which are different from the phenomenological minima. Moreover, they are not always highly symmetric, thus casting some doubt on the customary biased search scheme, which consists in relaxing with density functional theory global minima chosen among high symmetry structures obtained by means of phenomenological potentials.     

THEORETICAL APPROACHES TO PROTEIN STRUCTURE-FUNCTION ANALYSIS (Ⅰ)——DIRECTED PERTURBATION CONFORMATIONAL ANALYSIS

A new computational technique called directed perturbation conformational analysis has been developed for use in protein model building and structure-function studies. Designed to perform an efficient local search of a macromolecular potential energy surface, the algorithm can be used to locate multiple energy minimum conformers via low energy transition state structures from a single starting or trial structure. The algorithm contains developments to stabilize transition state optimizations for systems described by many degrees of freedom displaying anharmonic potential energy surfaces. It has been found to be efficient in the generation of alternative equilibrium structures from a given trial structure when compared with those generated from a standard molecular dynamics simulation of N-acetyl, N'-methyl-deca-L-alaninamide.     

Dynamical consequences of symmetry breaking in benzene and difluorobenzene

The systems benzene/benzene-d(1) and o-/m-/p-difluorobenzene were studied in the dense gas phase with ultrafast transient absorption spectroscopy to investigate the effect of symmetry reduction through monodeuteration and constitutional isomerism on the timescales of intramolecular vibrational energy redistribution (IVR). In both systems IVR proceeds faster in the molecules of lower symmetry. In addition the dynamics were simulated in vibrational quantum number space using a simple model based on scaling state-to-state interactions by coupling order and the energy gap law. These simulations (semi-) quantitatively reproduce the experimental data for benzene and benzene-d(1) without incorporating further molecular symmetry restrictions. The relative impact of molecular symmetry and vibrational state space structure on IVR is discussed.     

Identification of conical structures in small aluminum oxide clusters: infrared spectroscopy of (Al2O3)1-4(AlO)+

The vibrational spectroscopy of the electronically closed-shell (Al 2O 3) n (AlO) (+) cations with n = 1-4 is studied in the 530-1200 cm (-1) range by infrared predissociation spectroscopy of the corresponding ion-He atom complexes in combination with quantum chemical calculations. In all cases we find, assisted by a genetic algorithm, global minimum structures that differ considerably from those derived from known modifications of bulk alumina. The n = 1 and n = 4 clusters exhibit an exceptionally stable conical structure of C 3 v symmetry, whereas for n = 2 and n = 3, multiple isomers of lower symmetry and similar energy may contribute to the recorded spectra. A blue shift of the highest energy absorption band is observed with increasing cluster size and attributed to a shortening of Al-O bonds in the larger clusters. This intense band is assigned to vibrational modes localized on the rim of the conical structures for n = 1 and n = 4 and may aid in identifying similar, highly symmetric structures in larger ions.     

Generalized chirality and symmetry deficiency

Some of the elementary properties of molecular electron densities are studied from the perspectives of generalizations of symmetry, symmetry deficiency, and in particular, chirality. A simple, information‐theoretical proof of the Hohenberg–Kohn theorem is discussed, and the information contents of local and global molecular electron densities are compared using a formulation of quantum chemistry on a compact manifold. One result, the “holographic electron density theorem”, involving a compactification step combined with analytic continuation, gives a tool for comparing local and global symmetry properties. The compact manifold quantum chemistry approach leads to a precise statement on the role of local molecular regions in determining global properties of complete, boundaryless molecules, resulting in constraints on their symmetry, chirality, and other types of symmetry deficiencies. A special similarity measure, the SLT measure, is used for generalized density domain comparisons, suitable in general for the comparison of semilattices with a tree structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structure,spectroscopy and electronic properties of neutral lattice-like (MgO) n clusters: a study based on a blending of DFT with stochastic algorithms inspired by natural processes

In this article, we explore the feasibility of using stochastic optimization techniques, which are inspired by natural processes, namely simulated annealing (SA) and genetic algorithm (GA) in association with DFT, to find out the global minimum structures of (MgO) _n clusters with n being in the range of 2–15. To check whether the structures are indeed the correct ones, we proceed to do several property calculations like IR-spectroscopic modes, vertical excitation energy, cluster-formation energy, vertical ionization potential, the HOMO–LUMO gap as well as polarizability and hyperpolarizability—both static and dynamic. We emphasize on the point that an initial determination of structure using SA/GA leads to very quick relaxation to structures which are very close to the structures predicted from quantum chemical calculations done from the outsets like DFT. The general pattern of these systems to form beautiful three-dimensional lattice networks is also evident from our study.     

Understanding topological symmetry: a heuristic approach to its determination

An algorithm based on heuristic rules for topological symmetry perception of organic structures having heteroatoms, multiple bonds, and any kind of cycle, and configuration, is presented. This algorithm identifies topological symmetry planes and sets of equivalent atoms in the structure, named symmetry atom groups (SAGs). This approach avoids both the need to explore the entire graph automorphism groups, and to encompass cycle determination, resulting in a very effective computer processing. Applications to several structures, some of them highly symmetrical such as dendrimers, are presented.     

Molecular mechanics conformational analysis of cyclononane using the RIPS method and comparison with quantum-mechanical calculations

The recently reported Random Incremental Pulse Search (RIPS) technique has been used to probe the conformational energy surface of cyclononane. The stochastic method permits searching of the potential energy surface for all minimum-energy conformations. The search located all previously reported structures together with three additional conformations that were not found by earlier, primitive searching techniques. Two of these structures are high-nergy skew forms, and the third is a low-energy conformer that should contribute significantly to the overall equilibrium set of cyclononane conformations. The global minimum has been found to be the D₃ symmetrical twist chair-boat (TBC) form in accordance with previous studies. The newly discovered low-energy structure, which lies only 2.2 kcal/mol above the global minimum, has been designated twist chair-twist chair (TCTC). The two higher energy conformers are skewed chair-chair (SCC) and skewed boat-boat (SBB) forms that are 5.7 kcal/mol and 10.4 kcal/mol above the global minimum, respectively. The seven reported conformations were reanalyzed quantum mechanically (AM 1), and a comparison between MM 2 and AM 1 results is presented.     

Beyond two-state conical intersections. Three-state conical intersections in low symmetry molecules: the allyl radical

Using multireference configuration interaction expansions comprised of over 7 million configuration state functions, three-state conical intersections are reported for the closely spaced, spectroscopically observed (tilde)B(2A1), (tilde)C(2B1), and (tilde)D(2B2) states (in C(2v) symmetry) of the allyl radical. These conical intersections of states which were previously assigned as the 3,4,5(2)A states and are here reassigned as the 4,5,6(2)A states, are expected to be accessible using optical probes. This conclusion is obtained from the structure of the minimum energy point on the 4,5,6(2)A three-state conical intersection seam which is similar to the equilibrium structure of the ground (tilde)X(2A2) state and only 1.1 eV above the (tilde)D(2B2) state at its equilibrium geometry. The seam of three-state degeneracies joins two two-state seams of conical intersection, the 4,5(2)A and 5,6(2)A conical intersection seams. The energy of the minimum energy point on the 4,5(2)A two-state seam is only 0.15 eV above that of the (tilde)D(2B2) state at its equilibrium structure. Three-state intersections are also reported for the 3,4,5(2)A states.     

Different approaches to conformational analysis: A comparison of completeness,efficiency, and reliability based on the study of a nine-membered lactam

Different methods such as molecular dynamics, systematic, or stochastic search and a special “generic shape” algorithm have been employed in the conformational analysis of a nine-membered lactam. Furthermore, crystal data were used to generate conformations of the compound under consideration. The various methods are compared in terms of their efficiency and completeness in the search for conformations with an energy content of up to 60 kJ/mol above the global minimum. Additionally, the generated conformations have been optimized by different techniques, molecular mechanics and quantum chemical calculations, to compare the number of existing local minima and their relative energies and geometries.     

Invariance criteria and symmetry conservation rules for geometry optimizations

The objective of this paper is to analyze the behaviour of some minimization methods such as steepest descent method, generalized Newton and quasi-Newton methods under transformations of the variables of the function to be minimized. Energy and molecular coordinates are the function and the variables, respectively, in the case of geometry optimizations. Invariant levels are shown to be decisive for the area where the minimization methods can be successfully employed without rescaling of the coordinates. Specific conditions for symmetry conservation are worked out in context of invariant levels. Symmetry making, breaking and conservation are shown with working examples of geometry optimizations and calculation of energy minimum paths on the basis of certain kinds of molecular coordinates.     

Ab initio crystal structure prediction-I. Rigid molecules

A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented. The approach is based on the global minimization of the lattice enthalpy of the crystal. The modeling of the electrostatic interactions is accomplished through a set of distributed charges that are optimally and automatically selected and positioned based on results of quantum mechanical calculations. A four-step global optimization algorithm is used for the identification of the local minima of the lattice enthalpy surface. A parallelized implementation of the algorithm permits a much more extensive search of the solution space than has hitherto been possible, allowing the identification of crystal structures in less frequently occurring space groups and with more than one molecule in the asymmetric unit. The algorithm has been applied successfully to the prediction of the crystal structures of 3-aza-bicyclo(3.3.1)nonane-2,4-dione (P2(1)/a, Z' = 1), allopurinol (P2(1)/c, Z' = 1), 1,3,4,6,7,9-hexa-azacycl(3.3.3)azine (Pbca, Z' = 2), and triethylenediamine (P6(3)/m, Z' = 1). In all cases, the experimentally known structure is among the most stable predicted structures, but not necessarily the global minimum.     

Force field development for poly(dimethylsilylenemethylene) with the aid of ab initio calculations

The molecular geometries, conformational energies, and zero-point energies of di(trimethylsilylene)methylene have been determined from high-level quantum chemistry calculations. The results are further used in the parametrization of a classical potential energy function suitable for performing simulations of the corresponding polymer, namely, poly(dimethylsilylenemethylene). Di(trimethylsilylene)methylene geometrical parameter optimizations for a proper location of the global minimum and other local minima, constrained at certain dihedral and bond angles, were performed at both the B3LYP/6-311G and MP2(full)/6-311G levels of theory. The global minimum configuration is slightly displaced from a perfectly staggered geometry, approximately by 16.0 degrees, at both levels of theory. Molecular mechanics and Monte Carlo calculations for isolated polymer chains together with molecular dynamics runs for the modeled dimer provide very good results in terms of conformational and thermodynamic properties.     

CAESAR: a new conformer generation algorithm based on recursive buildup and local rotational symmetry consideration

A highly efficient conformer search algorithm based on a divide-and-conquer and recursive conformer build-up approach is presented in this paper. This approach is combined with consideration of local rotational symmetry so that conformer duplicates due to topological symmetry in the systematic search can be efficiently eliminated. This new algorithm, termed CAESAR (Conformer Algorithm based on Energy Screening and Recursive Buildup), has been implemented in Discovery Studio 1.7 as part of the Catalyst Component Collection. CAESAR has been validated by comparing the conformer models generated by the new method and Catalyst/FAST. CAESAR is consistently 5-20 times faster than Catalyst/FAST for all data sets investigated. The speedup is even more dramatic for molecules with high topological symmetry or for molecules that require a large number of conformers to be sampled. The quality of the conformer models generated by CAESAR has been validated by assessing the ability to reproduce the receptor-bound X-ray conformation of ligands extracted for the Protein Data Bank (PDB) and assessing the ability to adequately cover the pharmacophore space. It is shown that CAESAR is able to reproduce the receptor-bound conformation slightly better than the Catalyst/FAST method for a data set of 918 ligands retrieved from the PDB. In addition, it is shown that CEASAR covers the pharmacophore space as well or better than Catalyst/FAST.     

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.