From Cyclo[18]carbon to the Novel Nanostructures-Theoretical Predictions.

In this paper, we present a number of novel pure-carbon structures generated from cyclo[18]carbon. Due to the very high reactivity of cyclo[18]carbon, it is possible to link these molecules together to form bigger molecular systems. In our studies, we generated new structures containing 18, 36 and 72 carbon atoms. They are of different shapes including ribbons, sheets and tubes. All these new structures were obtained in virtual reactions driven by external forces. For every reaction, the energy requirement was evaluated exactly when the corresponding transition state was found or it was estimated through our new approach. A small HOMO-LUMO gap in these nanostructures indicates easy excitations and the multiple bonds network indicates their high reactivity. Both of these factors suggest that some potential applications of the new nanostructures are as components of therapeutically active carbon quantum dots, terminal fragments of graphene or carbon nanotubes obtained after fracture or growing in situ in catalytic reactions leading to the formation of carbonaceous materials.

The carbohydrate glycosylphosphatidylinositol anchor chain under mechanical stress.

Carbohydrates have quite complicated micro heterogenic structure which may undergo different structural transitions. Due to their extreme flexibility it is very difficult to investigate such structural changes experimentally. In these studies we want to predict what structural and conformational changes are possible in the carbohydrate glycosylphosphatidylinositol anchor chain (GPI): the tetrasaccharide with the unique sequence Man-α(1 → 2)-Man-α(1 → 6)-Man-α(1 → 4)-GlcN-α. This is a very important biomolecule associated with the processes of transmitting various types of signals in the cells of living organisms. In order to investigate conformational and structural changes in GPI we use in these studies the theoretical Enforced Geometry Optimization (EGO) method. In this method a molecule is exposed to a mechanical stress caused by external forces applied to selected atoms. It turned out that under external stretching forces the mannopyranose unit can change its 4C1 chair conformation into three different forms: 1S3, oS2 and B2,5. The initial 4C1 glucosamine ring can transit into the twisted boat 1S3 and the boat Bo,3 conformations. The obtained results confirm the high flexibility of the GPI anchor sugar chain.

Search for transition states with external forces.

It is much more difficult to find on the potential energy surface (PES) a transition state (TS) than a local minimum (LM). We propose a new methodology which makes this task much easier. Applying external forces to nuclei in a molecule we can locate on PES not just one particular TS but a number of consecutive transition states. With our approach it is possible to move over PES from one transition state to another without involving any local minima. The latter can be located in a separate step through the reaction path calculations performed for every transition state found before. Preliminary results for the 2-fluorofuran molecule illustrate the usefulness of the proposed method.

Protonation of Cytosine-Rich Telomeric DNA Fragments by Carboxylated Carbon Nanotubes: Insights from Computational Studies.

In this work, we studied, using computational methods, the protonation reactions of telomeric DNA fragments being due to interaction with carboxylated carbon nanotubes. The applied computational methodology is divided into two stages. (i) Using classical molecular dynamics, we generated states in which carboxyl groups are brought to the vicinity of nitrogen atoms within the cytosine rings belonging to the DNA duplex. (ii) From these states, we selected two systems for systematic quantum chemical studies aimed at the analysis of proton-transfer reactions between the carboxyl groups and nitrogen atoms within the cytosine rings. Results of molecular dynamics calculations led to the conclusion that sidewall-functionalized carbon nanotubes deliver carboxyl groups slightly more effectively than the on-tip-functionalized ones. The latter can provide carboxyl groups in various arrangements and more diverse quality of approach of carboxyl groups to the cytosines; however, the differences between various arrangements of carboxyl groups are still not big. It was generally observed that narrow nanotubes can access the cytosine pocket easier than wider ones. Quantum chemical calculations led however to the conclusion that a direct proton transfer from the carboxyl group to the nitrogen atom within the cytosine ring is impossible under normal conditions. Precisely, we detected either very high activation barrier for the proton-transfer reaction or instability of the reaction product, i.e., its spontaneous decomposition toward reaction substrates.

Simulation of the conformational flexibility of the mycodextran under external forces.

Mycodextran-also known as nigeran-is an unbranched polysaccharide made of α-d-glucopyranose units alternatively connected by (1 → 3) and (1 → 4) glycosidic linkages produced intracellularly by Aspergillus niger and Penicillium crustosum. In this work we examine possible enforced conformational transitions in the glucopyranose rings in the nigeran oligosaccharide chains. In order to simulate such structural changes we used the Enforced Geometry Optimization (EGO) method.

Isomerization and Decomposition of 2-Methylfuran with External Forces.

The primary goal of this project was to evaluate the performance of the Standard and Enforced Geometry Optimization (SEGO) method which we have recently developed. The SEGO method has been designed for an automatic location of multiple minima on the molecular Potential Energy Surface (PES), and its usefulness has been demonstrated so far for three molecules only. In this project we applied the SEGO method to explore the 2-methylfuran (2MF) PES. Our choice was not accidental: this molecule recently gained a great deal of interest as a potential candidate for biofuel, and therefore its pyrolysis is extensively studied. To understand pyrolysis of 2MF a detailed knowledge about its PES is needed. In these studies we explored the 2MF PES and located a surprisingly large number of local minima corresponding to 2MF isomers and decomposition products. Some of the 2MF isomers and fragments have amazing structures which most likely were previously unknown. All structures presented in this paper were found in an automatic manner as a result of the enforced chemical reactions driven by the SEGO method. Thus, in these studies we have not only proven that the SEGO method is a very efficient tool for exploring molecular potential energy surfaces, but we also obtained very detailed knowledge about the 2MF PES.

Exploring Potential Energy Surface with External Forces.

We present a new method that allows automatic location of multiple local minima on the molecular potential energy surface (PES). Standard geometry optimization procedures converge to a local minimum on the PES. They can be forced to penetrate other regions of the potential surface by applying external forces to nuclei in a molecule. One specific choice of such external forces is proposed in this paper, and preliminary results demonstrating its usefulness are presented.

Theoretical studies of the pyranose ring under mechanical stress.

In this work we use our Enforced Geometry Optimization (EGO) method to investigate conformational transitions in the pyranose ring under mechanical stress caused by external forces. We examine possible transitions and/or inversions induced by external forces in the pyranose ring in the chair conformation with two axial glycosidic bonds. The results obtained provide new insight into the mechanism of the conformational transitions which strongly depends on substituents present in a pyranose ring. We also conclude that interpretation of AFM force-extension curves is not necessarily straightforward; not every plateau there corresponds to a conformational transition and not every transition can be clearly seen as a plateau.

Approximate Force Constants from Uncoupled Self-Consistent Field Perturbation Theory Using Nonhybrid Density Functional Theory.

Second derivatives of the molecular energy with respect to the nuclear coordinates (the nuclear Hessian or force constant matrix) are important for predicting infrared and Raman spectra, for calculating thermodynamic properties, for characterizing stationary states, and for guiding geometry optimization. However, their calculation for larger systems scales with molecular size one power higher than the calculation of the energy and the forces. The step responsible for the steep scaling of the nuclear Hessian is the coupled-perturbed self-consistent field (CP-SCF) iteration. This is omitted in the uncoupled SCF (UC-SCF) approximation. We have found that, though UC-SCF performs rather poorly at the Hartree-Fock and hybrid DFT levels, its performance for "pure" (non-hybrid) DFT is remarkably good. This is valid also for imaginary frequencies that characterize transition states. UC-SCF vibrational frequencies and normal modes are compared with coupled calculations for various exchange-correlation functionals including Hartree-Fock, and with basis sets ranging from simple to large for a variety of organic and some organometallic molecules. Their unexpectedly good performance makes them good candidates for calculating thermodynamic properties and for guiding difficult geometry optimizations, including the determination of transition states.

Simulation of force spectroscopy experiments on galacturonic acid oligomers.

Pectins, forming a matrix for cellulose and hemicellulose, determine the mechanics of plant cell walls. They undergo salient structural changes during their development. In the presence of divalent cations, usually calcium, pectins can form gel-like structures. Because of their importance they have been the subject of many force spectroscopy experiments, which have examined the conformational changes and molecular tensions due to external forces. The most abundant unit present in the pectin backbone is polygalacturonic acid. Unfortunately, experimental force spectroscopy on polygalacturonic acid molecules is still not a trivial task. The mechanism of the single-molecule response to external forces can be inferred by theoretical methods. Therefore, in this work we simulated such force spectroscopy experiments using the Enforced Geometry Optimization (EGO) method. We examined the oligomeric (up to hexamer) structures of α-D-galacturonic acid exposed to external stretching forces. The EGO simulation of the force spectroscopy appropriately reproduced the experimental course of the enforced conformational transition: chair →inverted chair via the twisted boat conformation(s) in the pyranose ring of α-D-galacturonic acid. Additionally, our theoretical approach also allowed to determine the minimum oligomer size adequate for the description of nano-mechanical properties of (poly)-α-D-galacturonic acid.

An efficient parallel algorithm for the calculation of unrestricted canonical MP2 energies.

We present details of our efficient implementation of full accuracy unrestricted open-shell second-order canonical Møller-Plesset (MP2) energies, both serial and parallel. The algorithm is based on our previous restricted closed-shell MP2 code using the Saebo-Almlöf direct integral transformation. Depending on system details, UMP2 energies take from less than 1.5 to about 3.0 times as long as a closed-shell RMP2 energy on a similar system using the same algorithm. Several examples are given including timings for some large stable radicals with 90+ atoms and over 3600 basis functions.

Isomerization of stilbene using enforced geometry optimization.

Using our recently proposed quantum chemical model to simulate the effect of external forces acting on a molecule (Wolinski and Baker, Mol Phys 2009, 107, 2403), which we subsequently termed enforced geometry optimization (EGO), we investigate structural isomerism in C(14) H(12) , starting from cis-stilbene. By applying an external force to pairs of carbon atoms, one from each "half" of the molecule, we have generated 10 different structural isomers. Each was characterized as a minimum by vibrational analysis. Not only can EGO generate potentially new, metastable isomers it can also provide good initial guesses for transition states connecting the starting and final structures, thus giving an estimate of the stability of the new isomers to rearrangement back to the starting material. In addition to the new isomers, we provide a full set of vibrational fundamentals for cis- and trans-stilbene and 4a,4b-dihydrophenanthrene. The agreement with experimental assignments is excellent, with mean average deviations for the stilbenes of 5.0 cm(-1) or less.

Kinetically stable high-energy isomers of C14H12 and C12H10N2 derived from cis-stilbene and cis-azobenzene.

Following on from our recent enforced geometry optimization (EGO) investigation of isomerization in cis-stilbene (J Comput Chem, in press) we report the discovery of two interesting new, symmetrical "fused sandwich" isomers of both cis-stilbene and the related cis-azobenzene. The isomers were obtained by applying external forces to pairs of carbon atoms from each of the benzene rings in cis-stilbene and cis-azobenzene simultaneously, and are all at least 100 kcal mol(-1) higher in energy than the starting material. Each new structure was characterized as a minimum by vibrational analysis. Despite their high energy, all of the new isomers appear to be kinetically stable with respect to rearrangement back to cis-stilbene or cis-azobenzene, respectively.

Instability of 2,2-di(pyridin-2-yl)acetic acid. Tautomerization versus decarboxylation.

The DFT calculations at the B3LYP level with 6-311G** basis set were carried out in order to reveal whether tautomerization or decarboxylation is responsible for the instability of 2,2-di(pyridin-2-yl)acetic (DPA) and 1,8-diazafluorene-9-carboxylic (DAF) acids. The carboxyl protons in both compounds are involved in the intramolecular hydrogen bonds (the pyridine nitrogen atoms are the hydrogen bond acceptors). Although formation of two intramolecular OH · · · N hydrogen bonds in the enols of both carboxylic acids enables effective electron delocalization within the quasi rings (· · · HO - C = C - C = N), only ene-1,1-diol of DAF has somewhat lower energy than DAF itself (ΔE is ca. 7 kcal mol(-1)). DPA and its enediol have comparable energies. Migration of the methine proton toward the carbonyl oxygen atom (to form enediols) requires overstepping the energy barriers of 55-57 kcal mol(-1) for both DPA and DAF. The enaminone tautomers of the acids, formed by migration of this proton toward the pyridine nitrogen atom, are thermodynamically somewhat more stable than the respective enediols. The energy barriers of these processes are equal to ca. 44 and 62 kcal mol(-1) for DPA and DAF, respectively. Thus, such tautomerization of the acids is not likely to proceed. On the other hand, the distinct energetic effects (ca. 15 kcal mol(-1)) favor decarboxylation. This process involves formation of (E)-2-(pyridin-2(1H)-ylidenemethyl)pyridine and its cyclic analogue followed by their tautomerization to (dipyridin-2-yl)methane and 1,8-diazafluorene, respectively. Although the later compound was found to be somewhat thermodynamically more stable, kinetic control of tautomerization of the former is more distinct.

Theoretical analysis of solvent effects on nitrogen NMR chemical shifts in oxazoles and oxadiazoles.

Using quantum chemistry methods we have evaluated the solvent effects on the (14)N NMR chemical shifts in five oxa- and oxadiazoles dissolved in twelve solvents. These solvents differ in their polarity with the dielectric constants varying from 2 to 80. Moreover, three of them have a hydrogen-bond donor character. All possible hydrogen-bonding in the water solution with the oxygen and nitrogen (hydrogen-acceptor) centers in oxazoles (2) and oxadiazoles (3) have been considered in our studies. It has been shown that both the pure solvent and hydrogen-bonding effects are significant and result in (14)N magnetic shielding increase. In water solutions the pure solvent effect is larger than the hydrogen-bonding effect. In addition, the solvent effect has been analyzed in terms of its direct and indirect contributions. It should be emphasized that our theoretical results for (14)N chemical shifts in oxa- and oxadiazoles remain in a very good agreement with the accurate experimental data.

Parallel DFT gradients using the Fourier Transform Coulomb method.

The recently described Fourier Transform Coulomb (FTC) algorithm for fast and accurate calculation of Density Functional Theory (DFT) gradients (Füsti-Molnar, J Chem Phys 2003, 119, 11080) has been parallelized. We present several calculations showing the speed and accuracy of our new parallel FTC gradient code, comparing its performance with our standard DFT code. For that part of the total derivative Coulomb potential that can be evaluated in plane wave space, the current parallel FTC gradient algorithm is up to 200 times faster in total than our classical all-integral algorithm, depending on the system size and basis set, with essentially no loss in accuracy. Proposed modifications should further improve the overall performance relative to the classical algorithm.

An efficient atomic orbital based second-order Møller-Plesset gradient program.

Based on the orbital-invariant atomic orbital formulation of the MP2 (Møller-Plesset second-order perturbation theory) energy and gradient [P. Pulay and S. Saebø, Theor. Chim. Acta 69, 357 (1986)], we have derived and programmed detailed working equations for closed-shell MP2 gradients. The orbital-invariant form avoids the difficulties of other formulations with frozen orbitals, and allows the use of arbitrary occupied orbitals, an important consideration for local correlation theories, although the present program uses canonical molecular orbitals. The atomic orbital formulation offers savings both in storage and computer time. Test calculations on systems containing up to approximately 100 atoms and approximately 1000 basis functions, performed on a single personal computer, are reported. Parallelization of the code is underway.

Parallel stored-integral and semidirect Hartree-Fock and DFT methods with data compression.

Recent developments in magnetic disk technology have made stored-integral techniques competitive with the currently more widely used direct methods, which involve the recalculation of the basic two-electron integrals. We present efficient conventional (all integrals stored) and semidirect Hartree-Fock and DFT algorithms with data compression for single-processor and distributed memory parallel computers, and compare them with the corresponding direct algorithms. On inexpensive modern personal computer-based hardware, the stored integral method is up to three times more efficient than the direct method in terms of total elapsed job time.