The multiple minimum problem in molecular modeling. Tree searching internal coordinate conformational space

A general algorithm is described which exhaustively searches conformational space using an internal coordinate tree search. Using only geometrical operations and a set of criteria for eliminating chemically unreasonable structures, the algorithm generates starting geometries for optimization by molecular mechanics. An implementation of this algorithm is exceedingly fast and finds all known minima, as well as several new ones, for four test alkanes. This method makes feasible global conformational searches for molecules with up to 10⁹ conformational possibilities.     

Conformational searching methods for small molecules. II. Genetic algorithm approach

We demonstrate the use of a genetic algorithm (GA) search procedure for finding low-energy conformations of small to medium organic molecules (1–12 rotatable bonds). GAS are in a class of biologically motivated optimization methods that evolve a population of individuals where individuals who are more “fit” have a higher probability of surviving into subsequent generations. Here, an individual is a conformation of a given molecule and the fitness is the molecule's conformational energy. In the course of a simulated evolution, the population produces conformations having increasingly lower energy. We test the GA method on a suite of 72 molecules and compare the performance against the CSEARCH algorithm in Sybyl. For molecules with more than eight rotatable bonds, the GA method is more efficient computationally and as the number of rotatable bonds increases the relative efficiency of the GA method grows. The GA method also found energies equal to or lower than the energy of the relaxed crystal structure in the large majority of cases. © John Wiley & Sons, Inc.     

Torsional symmetry dependence of S1 dynamics in molecules that undergo methyl internal rotation

The single‐rovibronic‐level fluorescence of “intermediate‐case” molecules that undergo methyl internal rotation is strongly influenced by the torsional symmetry of the lowest excited singlet state (S₁). The most dramatic example of such symmetry dependence comes from our recent finding that the intensities of the e–e transitions in the high‐resolution S₁←S₀ fluorescence excitation spectra of jet‐cooled acetaldehyde become very weak relative to the a–a transitions at higher beam temperatures. In this study, we rationalize this remarkable torsional symmetry dependence of electronic relaxation in acetaldehyde on the basis of internal‐overall rotation coupling that leads to symmetry‐selective increase in the density of states for singlet‐triplet coupling. Related observations by others on aliphatic carbonyls and diazabenzenes are also discussed within the context of the coupling between the internal and overall rotation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 167–176, 1999     

Conformational dynamics of polypeptides and proteins in the dihedral angle space and in the cartesian coordinate space: Normal mode analysis of deca-alanine

Effects of different treatments of the degrees of freedom of bond length stretching and bond angle bending in computational analysis of conformational dynamics of proteins and polypeptides are assessed. More specifically, the normal mode analysis of conformational dynamics of α-helix of deca-alanine has been carried out both in the dihedral angle space (DAS) and in the Cartesian coordinate space (CCS). Almost perfect one-to-one correspondence has been found between normal modes in the CCS with frequencies less than 128 cm^?1 and those in the DAS with frequencies less than 164 cm^?1. Patterns of atomic displacements in the corresponding modes are very similar. This indicates that the effects of fixing degrees of freedom of bond length stretching and bond angle bending on the very-low-frequency normal modes in the CCS with frequencies less than 128 cm^?1 are almost solely to increase the frequencies by about 20%. The conclusion indicates that the different treatment of these degree does not lead to qualitatively different results as long as low-frequency motions are concerned. Based on the results of calculation, mechanical property of the α-helix of deca-alanine is discussed.     

Conformational searching of transition metal compounds

To date, no conformational search of inorganic complexes has been reported that searches for all the conformations and configurations available to the complex. This is due to the various coordination geometries that transition metal ions can adopt and the difficulties in conducting conformational searches with systems that have connected ring systems, such as the ones formed when a metal ion binds a multidentate ligand. Using three test complexes {[Co(dien)₂]³⁺, [Co(dien)(dpt)]³⁺, and [Co(hexamethylcyclam)(Cl)} the ability of the random kick (Cartesian stochastic Monte Carlo search) method and the Monte Carlo dihedral and positional method to find all conformations and geometric isomers was tested (dien, diethylenetriamine; dpt, di(3-aminopropyl)amine; hexamethylcyclam: tet-a, meso-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane; tet-b, racemic-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane). Both methods are significant improvements on the current method by which all possible isomers are entered graphically and minimized individually. The major difficulty that was encountered was how to differentiate between the large number of similar conformations found. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1549–1558, 1999     

Conformational searching methods for small molecules. I. Study of the sybyl search method

Several methods are available in the literature for the conformational analysis of small molecules. Each of these methods has some advantages and some disadvantages. Also, each of these methods may be expected to perform better or worse on different types of molecules. There is no clear calibration of each of these methods against a “standardized” set of molecules available in the literature. Such a reference work would be useful to the community because it would allow the choice of methods to be based on some facts. We attempted to provide a start to such a calibration in this article with an examination of the SYBYL SEARCH method. Methods for evaluating the performance of this method are described in detail and will be applied to all other available conformational analysis methods in future papers. © John Wiley & Sons, Inc.     

Incorporation of bond-length constraints in Monte Carlo simulations of cyclic and linear molecules: Conformational sampling for cyclic alkanes as test systems

A simple method for incorporating bond-length constraints in Monte Carlo simulations of cyclic and linear molecules is described. As an example, the conformational behavior of five even-numbered cyclic alkanes is studied using Monte Carlo simulation and the MM2 force field. © 1994 by John Wiley & Sons, Inc.     

Conformational analysis of nucleic acid molecules with flexible furanose rings in dihedral angle space

The computational algorithm that works in the coordinate space of dihedral angles (i.e., bond lengths and bond angles are kept fixed and only rotatable dihedral angles are treated as independent variables) is extended to deal with the pseudorotational m otion of furanose rings by introducing a variable of pseudorotation. Then, this algorithm is applied to a distance geometry calculation that generates three-dimensional (3D) structures that are consistent with given constraints of interatomic distances. This method efficiently generates 3D structures of an RNA hairpin loop which satisfy a set of experimental NMR data. © 1996 by John Wiley & Sons, Inc.     

Conformational searching methods for small molecules. III. Study of stochastic methods available in SYBYL and MACROMODEL

In a continuing effort to provide the computational community with a reference work comparing all of the available conformer searching methods, we have exposed the standard set of small molecules to two commonly used stochastic searching techniques. Advantages and limitations of these methods are discussed. © 1996 by John Wiley & Sons, Inc.     

Conformational analysis of aromatic molecules

The mechanical model used in conformation calculations is discussed. A method is developed for strained aromatic systems with possible out-of-plane deformations. An approximate analysis is presented to reveal criteria for planarity.     

Torsional isomerization of biologically active bicyclic molecules

Rotational isomerization of bipyridines C₅H₄N? C₅H₄N was studied by CNDO /2, PPP /CI , and CNDO /CI methods. It is shown that CNDO /2 overestimates the angle of rotation ? between the pyridine rings ca. two times. The angle ? was determined for 2,2′-bipyridine by means of correlation of the theoretical (CNDO /2) and experimental dipole moment. It was also found from the correlation between the theoretical and experimental UV spectra. It is shown that there is an explicit dependence of the results upon the distance between heteroatoms (PPP /CI ). It has been found that the CNDO /CI method correctly predicts the value of the rotational angles and their sequence in bipyridines.     

Conformational stability,barriers to internal rotation,normal coordinate analysis,and vibrational assignment of chloroacetyl bromide

The infrared spectra (3200 to 30 cm^–1) of gaseous and solid chloroacetyl bromide, CH₂ClC(O)Br, and the Raman spectra (3200 to 10 cm^–1) of the gas, liquid (with depolarization data), and solid have been recorded. From the observed asymmetric torsional transitions, the potential function governing internal rotation of the CH₂Cl moiety has been determined with the following coefficients:V ₁=336±11,V ₂=73±10,V ₃=757+7,V ₄=103±3, andV ₆=5±2 cm^–1. This potential function is consistent with s-trans to gauche and gauche to gauche barriers of 963±11 and 709±12cm^–1, respectively, and enthalpy difference of 373 ± 24 cm^–1 with the dihedral angle of the gauche rotamer being 115°. The enthalpy difference has been determined experimentally from the studies of the Raman spectra at different temperatures to be 359±68 cm^–1 (1.03±0.19 kcal mol^–1) and 507±24 cm^–1 (1.45±0.07 kcal mol^–1) for the gas and liquid, respectively, with the s-trans conformer being the more stable conformer in the gas and liquid and the only one present in the annealed solid. A complete assignment of the vibrational fundamentals is proposed from spectral data obtained for the gas, liquid, and solid. The assignment is supported by a normal coordinate calculation utilizing a modified valence force field to obtain the frequencies for the normal vibrations and the potential energy distribution. The results are discussed and compared to the corresponding quantities for some similar molecules.Taken in part from the thesis of H. V. Phan, which will be submitted to the Department of Chemistry in partial fulfillment of the Ph.D. degree.     

Dynamical and statistical effects of the intrinsic curvature of internal space of molecules

The Hamilton dynamics of a molecule in a translationally and/or rotationally symmetric field is kept rigorously constrained in its phase space. The relevant dynamical laws should therefore be extracted from these constrained motions. An internal space that is induced by a projection of such a limited phase space onto configuration space is an intrinsically curved space even for a system of zero total angular momentum. In this paper we discuss the general effects of this curvedness on dynamics and structures of molecules in such a manner that is invariant with respect to the selection of coordinates. It is shown that the regular coordinate originally defined by Riemann is particularly useful to expose the curvature correction to the dynamics and statistical properties of molecules. These effects are significant both qualitatively and quantitatively and are studied in two aspects. One is the direct effect on dynamics: A trajectory receives a Lorentz-like force from the curved space as though it was placed in a magnetic field. The well-known problem of the trapping phenomenon at the transition state is analyzed from this point of view. By showing that the trapping force is explicitly described in terms of the curvature of the internal space, we clarify that the physical origin of the trapped motion is indeed originated from the curvature of the internal space and hence is not dependent of the selection of coordinate system. The other aspect is the effect of phase space volume arising from the curvedness: We formulate a general expression of the curvature correction of the classical density of states and extract its physical significance in the molecular geometry along with reaction rate in terms of the scalar curvature and volume loss (gain) due to the curvature. The transition state theory is reformulated from this point of view and it is applied to the structural transition of linear chain molecules in the so-called dihedral angle model. It is shown that the curvature effect becomes large roughly linearly with the size of molecule.     

The generator coordinate approximation for molecules: A review

The generator coordinate approximation is a non-adiabatic theory of molecular systems. Its fundamental outlines were developed during the 1970's. A further analysis and first applications were published during the 1980's. In this paper, we review the present status of the theory.     

Conformational sampling of bioactive molecules: a comparative study

The necessity to generate conformations that sample the entire conformational space accessible to a given molecule is ubiquitous in the field of computer-aided drug design. Protein-ligand docking, 3D database searching, and 3D QSAR are three commonly used techniques that depend critically upon the quality and diversity of the generated conformers. Although there are a wide range of conformational search algorithms available, the extent to which they sample conformational space is often unclear. To address this question, we conducted a robust comparison of the search algorithms implemented in several widely used molecular modeling packages, including Catalyst, Macromodel, Omega, MOE, and Rubicon as well as our own method, stochastic proximity embedding (SPE). We found that SPE used in conjunction with conformational boosting, a heuristic for biasing conformational search toward more extended or compact geometries, along with Catalyst, are significantly more effective in sampling the full range of conformational space compared to the other methods, which show distinct preferences for either more extended or more compact geometries.     

Conformational analysis of unsaturated molecules: 1,4-cis-dichlorobutene-2

Infrared and Raman spectra have been obtained for 1,4 cis-dibromobutene-2 in the liquid, amorphous and crystalline phases. Normal coordinate calculations have been performed for several model conformations. These data show the SCS and SCS' conformations as the more stable isomers. The two isomers are seen to be of nearly equal energies on the basis of empirical nonbonded-atom calculations,In the crystalline state only one isomer (probably SCS) is found.     

Conformational analysis of six-membered cyclic carbonates

The conformational isomerization of 2-oxo-1,3-dioxane and its methyl analogs was investigated by means of ab initio RHF//6-31G(d,p) and MP2//6-31G(d,p) quantum-chemical methods. It is shown that in comparison with 1,3-dioxanes the potential energy surface of the mentioned compounds has a fewer number of stationary points and includes two minima corresponding to conformers of sofa or distorted sofa configuration and one maximum corresponding to 2,5-twist form. The value of potential barrier of interconversion of cyclic carbonates is significantly lower than that of the analogously substituted 1,3-dioxanes.