Variable step molecular dynamics: An exploratory technique for peptides with fixed geometry

A new algorithm is presented for performing molecular dynamics simulations of peptides with fixed geometry, with the aim of simulating conformational changes and of exploring conformational space. The principle of the method is to expand the potential energy as a Taylor's series in the coordinates around the current point, retaining the force and its first two derivatives, and obtain a series solution of the resulting differential equations using a method due to Lyapunov. By choosing the time step so that the second term in the series is small compared to the first, the true solution can in principle be approximated to any desired degree of accuracy. The algorithm has been used to solve numerically Lagrange's equations of motion for N-acetyl alanine amide and N-acetyl methionide amide, regarded as fixed at their C-termini, under the influence of the ECEPP/2 potential energy function, and time steps of 15–30 fsec have been achieved with little variation in the total energy. Possible directions for future development are discussed.     

Correlation of dihedral angles with 13C chemical shifts of quaternary carbon atoms of some phenothiazine derivatives

A direct relationship between the ¹³C nmr chemical shifts of the quaternary carbon atoms of the central ring of phenothiazine and the dihedral angle of the respective derivatives has been observed. This correlation allows for the useful and quick estimation of the dihedral angles of novel phenothiazines from readily obtainable ¹³C nmr solution measurements. In addition, the change in the dihedral angle appears to be directly related to the S-C_4a-C_10a bond angle; however, the C_4a-S-C_5a bond angle is not affected by changes in the dihedral angle. This indicates that the “flattening” of the phenothiazine tricyclic ring system is compensated for by the vertical displacement of the sulfur atom, by changes in hybridization of N₁₀, and by other angular distortions of the middle ring.     

High-temperature inorganic molecular species with polytopic bonds: I. Description in terms of potential energy surfaces

Nuclear distributions in complex inorganic molecules are described in terms of potential energy surfaces, calculated using a simple electrostatic model. The results of its application to the LiNC molecule agree satisfactorily with a priori quantum-mechanical calculations. Analysis of the data for CsNO₃, TIReO₄ and NaAlF₄ molecules leads to the conclusion that the polytopic nature of the bonds between the metal atom and the anion is the most important structural feature of these molecules. It is proposed that this behavior is a general feature of inorganic molecules of the type studied in this work.     

Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order

A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison with spin-free Dirac-Coulomb calculations indicates that the DPT series exhibits a smooth and monotonic convergence. The rate of convergence, however, depends on the charge of the involved nuclei and significantly slows down for heavy-element compounds.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.     

Direct perturbation theory in terms of energy derivatives: fourth-order relativistic corrections at the Hartree-Fock level

In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorporate in an additive manner scalar-relativistic and spin-orbit contributions, are given at the Hartree-Fock level and have been implemented in the CFOUR program package using the available analytic second-derivative techniques. The accuracy of the DPT4 corrections at the HF level is investigated by comparison with rigorous four-component calculations. Scalar-relativistic and spin-orbit contributions are analyzed individually and the importance of the various terms to those corrections is discussed. Furthermore, the basis-set dependence of the computed DPT4 corrections is investigated.     

Theoretical studies on a series of 1,2,3-triazoles derivatives as potential high energy density compounds

Based on the full-optimized molecular geometric structures at B3LYP/6-31G* and B3P86/6-31G* levels, the densities (ρ), detonation velocities (D), and pressures (P) for a series of 1,2,3-triazole derivatives, as well as their thermal stabilities, were investigated to look for high energy density compounds (HEDCs). The heats of formation (HOFs) are also calculated via designed isodesmic reactions. The calculations on the bond dissociation energies (BDEs) indicate that the BDEs of the initial scission step are between 53 and 70 kcal/mol, and 4-nitro-1,2,3-triazole is the most reactive compound, while 1-(2′,4′-dinitrophenyl)-5-nitro-1,2,3-triazole is the least reactive compound for 1,2,3-triazole derivatives studied. The condensed phase heats of formation are also calculated for the title compounds. These results would provide basic information for the further studies of HEDCs. The detonation data of 1-(3′,4′-dinitrophenyl)-4-nitro-1,2,3-triazole and 1-(2′,4′-dinitrophenyl)-4-nitro-1,2,3-triazole show that they meet the requirement for HEDCs.     

Computational DFT studies on a series of toluene derivatives as potential high energy density compounds

Based on the full optimized molecular geometric structures at B3LYP/6-31G**, B3LYP/6-31+G**, B3P86/6-31G**, and B3P86/6-31+G** levels, the densities (ρ), detonation velocities (D), and pressures (P) for a series of toluene derivatives, as well as their thermal stabilities, were investigated to look for high energy density compounds (HEDCs). The heats of formation (HOFs) are also calculated via designed isodesmic reactions. The calculations on the bond dissociation energies (BDEs) indicate that the BDEs of the initial scission step are between 48 and 59 kcal/mol, and pentanitrotoluene is the most reactive compound, while 2,4,6-trinitrotoluene is the least reactive compound for toluene derivatives studied. A good linear relationship between BDE/E and impact sensitivity is also obtained. The condensed phase HOFs are calculated for the title compounds. These results would provide basic information for the further studies of HEDCs. The detonation data of pentanitrotoluene show that it meets the requirement for HEDCs.     

Novel imidazole derivatives as potential agrochemicals: Synthetical and mechanistic studies

The importance of the imidazole nucleus is briefly outlined and some naturally occurring derivatives listed. The problem associated with direct alkylation on the imino nitrogen is discussed and synthesis of 1-alkyl derivatives by the thermal decarboxylation of 1-alkoxycarbonylimidazoles examined as a possible alternative. Spectroscopic investigation of this mechanism is reported. The fungal threat to plantains in the tropics by black siga-toka and the option of chemical control are discussed. Synthesis of potential fungicides are reported.     

Molecular chains with fixed bond lengths and angles: a study based on quantum statistical mechanics

This work studies large three-dimensional open molecular chains at thermal equilibrium in which bond lengths and angles are fixed (hard variables), based upon quantum statistics. A model for a chain formed by N particles interacting through harmonic-like vibrational potentials is treated in the high-frequency limit in which all bond lengths and angles become constrained, while other N angles (soft variables) remain unconstrained. The associated quantum partition function is bounded rigorously, using a variational inequality (related to the Born-Oppenheimer approximation), by another quantum partition function, Z. The total vibrational zero-point energy is shown to be independent of the soft variables thereby solving for this model a generic difficulty in the elimination of hard variables. Z depends only on soft variables and, under certain conditions, it can be approximated by a classical partition function Z_c. The latter satisfies the equipartition principle and it differs from other classical partition functions for related molecular chains. The extension of the model when only part of the bond angles become fixed in the high-frequency limit is outlined. As another generalization, a systematic study of macromolecules, as composed of electrons and heavy particles with Coulomb interactions, is also presented. Its exact quantum partition function is bounded, supposing that the effective molecular potential also tends to constrain all bond lengths and angles, and under suitable assumptions, by another quantum partition function. The latter depends only on the remaining soft variables and it generalizes the one obtained for the first model.     

The consistent force field: Representation of molecular structure by potential energy functions

The principles are outlined, but the presentation concentrates on: the choice of structures on which to optimise; accuracy of post-dicted structure; reliability of pre-dicted structure; model building from graphic data.     

Constrained numerical gradients and composite gradients: Practical tools for geometry optimization and potential energy surface navigation

A method is proposed to easily reduce the number of energy evaluations required to compute numerical gradients when constraints are imposed on the system, especially in connection with rigid fragment optimization. The method is based on the separation of the coordinate space into a constrained and an unconstrained space, and the numerical differentiation is done exclusively in the unconstrained space. The decrease in the number of energy calculations can be very important if the system is significantly constrained. The performance of the method is tested on systems that can be considered as composed of several rigid groups or molecules, and the results show that the error with respect to conventional optimizations is of the order of the convergence criteria. Comparison with another method designed for rigid fragment optimization proves the present method to be competitive. The proposed method can also be applied to combine numerical and analytical gradients computed at different theory levels, allowing an unconstrained optimization with numerical differentiation restricted to the most significant degrees of freedom. This approach can be a practical alternative when analytical gradients are not available at the desired computational level and full numerical differentiation is not affordable. © 2015 Wiley Periodicals, Inc.     

Simulations of lipid crystals: Characterization of potential energy functions and parameters for lecithin molecules

We evaluate an empirical potential energy function and associated parameters for classical molecular dynamics simulations of lecithins, a common class of lipid. The physical accuracy of the force field was tested through its application to molecular dynamics simulations of the known crystal structures of lipid molecules. Average atomic positions and molecular conformation are well maintained during the simulations despite considerable thermal motion. Calculated isotropic temperature factors correlate highly with those from experiment.     

New formulation for derivatives of torsion angles and improper torsion angles in molecular mechanics: Elimination of singularities

A new set of formulae is developed for the derivatives of torsion angle energy terms and is introduced into the program CHARMM. These formulae, which are based on derivatives of the torsion angle itself, avoid the singularities introduced by use of the derivatives of the torsion angle cosine. The potential energy can include any differentiable function of the torsion angle and there is no need for a special treatment for cases where planar conformations are not extrema. The resulting code is simpler than the original version and yields correct derivatives in all practical situations. Because the minimum of the torsion energy can be at any angle, the functionality of the existing energy routines is generalized. © 1996 by John Wiley & Sons, Inc.     

The geometry of small rings—IV: Molecular geometry of cyclopropene and its derivatives

Numeric structural data for 34 derivatives of cyclopropene and cyclopropenium ion have been retrieved from the Cambridge Crystallographic Database and analysed in conjunction with available gas-phase results. Geometric data indicate that the vinylic C atoms in cyclopropene use sp^1.19 hybrids in bond formation to substituents and contribute sp^2.68 hybridges to the ring σ-framework. The D_3h-symmetric cyclopropenium ion has a bond length of 1.373(3)Å, which can be related to distances in unstrained systems. Comparison of data for cyclopropenylidenes and 3,3-difluorocyclopropene with analogous cyclopropanes shows that π-donor effects (distal bond lengthening, vicinal bond shortening) are apparent in cyclopropene. Rehybridization and π-donation are largely responsible for cyclopropenylidene geometry, rather than significant contributions from dipolar and pseudo-aromatic resonance forms. Insufficient data exist to quantify the effect of π-acceptor substituents on cyclopropene, but some lengthening of vicinal bonds is apparent. Three major bonding patterns are exhibited by organomental derivatives of cyclopropenium and cyclopropene.     

Kinetic energy,potential energy,and virial ratio from calculations using systematic sequences of even-tempered basis sets

The use of systematic sequences of even-tempered basis sets in calculations of the kinetic energy, potential energy and virial ratio within the self-consistent-field molecular-orbital approach is discussed. The components of the total energy are shown to converge smoothly with increasing size of basis set. Systematic sequences of universal even-tempered basis sets are also considered.     

Boronated derivatives of protohemin IX with L-amino acids as potential anticancer agents

New water-soluble conjugates of protohemin IX with an anionic 1-carba-closo-dodecaborate polyhedron and L-amino acids have been synthesized. In these compounds, the amino acid residues are bound to the porphyrin ring through the amide or ester bond. The new water-soluble amino acid derivatives of boronated protohemin IX show high antitumor activity for human tumor cell lines.