Equilibrium Distance Research Articles

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 A), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.

Aluminum nitride graphene for DMMP nerve agent adsorption and detection

Using ab initio van der Waals density functional (vdW-DF) calculations, we investigate the adsorption of DMMP nerve agent on graphene, BN and AlN graphenes, involving full geometry optimization. Several active sites for both the interacting systems were considered in the adsorption process. The detailed analysis of the structural and electronical properties of energetically favorable configurations is carried out. The results show that adsorption of DMMP molecule on the Al site of the AlN graphene is energetically preferable. The calculated binding energy and equilibrium distance are about −0.74 eV (−72.34 kJ mol−1) and 2.035 Å, respectively, accompanying with charge transfer of 0.23 e. In addition, the P–O bond is rather significantly elongated when DMMP is adsorbed on AlN graphene. Compared to carbon graphene or BN graphene, the AlN graphene has stronger interaction with the DMMP molecule and can provide more sensitive signal for a single DMMP molecule. In particular, the semiconducting AlN graphene would become metallic after adsorption DMMP. Consequently, the AlN graphene is a promising candidate for the DMMP sensing and detection. Our ab initio vdW-DF findings present evidence for a rational benchmark for the applicability of the AlN graphene for DMMP adsorption and detection.

Insight into the description of van der Waals forces for benzene adsorption on transition metal (111) surfaces

Exploring the role of van der Waals (vdW) forces on the adsorption of molecules on extended metal surfaces has become possible in recent years thanks to exciting developments in density functional theory (DFT). Among these newly developed vdW-inclusive methods, interatomic vdW approaches that account for the nonlocal screening within the bulk [V. G. Ruiz, W. Liu, E. Zojer, M. Scheffler, and A. Tkatchenko, Phys. Rev. Lett. 108, 146103 (2012)] and improved nonlocal functionals [J. Klimeš, D. R. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)] have emerged as promising candidates to account efficiently and accurately for the lack of long-range vdW forces in most popular DFT exchange-correlation functionals. Here we have used these two approaches to compute benzene adsorption on a range of close-packed (111) surfaces upon which it either physisorbs (Cu, Ag, and Au) or chemisorbs (Rh, Pd, Ir, and Pt). We have thoroughly compared the performance between the two classes of vdW-inclusive methods and when available compared the results obtained with experimental data. By examining the computed adsorption energies, equilibrium distances, and binding curves we conclude that both methods allow for an accurate treatment of adsorption at equilibrium adsorbate-substrate distances. To this end, explicit inclusion of electrodynamic screening in the interatomic vdW scheme and optimized exchange functionals in the case of nonlocal vdW density functionals is mandatory. Nevertheless, some discrepancies are found between these two classes of methods at large adsorbate-substrate separations.

Direct-potential-fit analyses yield improved empirical potentials for the ground $X\,^1\Sigma _g^+$XΣg+1 state of Be2

We have performed new direct-potential-fit (DPF) analyses of the rotationally resolved A (1)Π(u)(ν'=2,3;J' =1,2)→X(1)Σ(+)(g) (ν" ∈[0,11];J" ∈[0,3]) stimulated emission pumping spectra of Be2 [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] using two quite different analytical potential energy functions that incorporate the correct theoretically known long-range behaviour in different ways. These functions are: the damped Morse/long-range potential [R. J. Le Roy, C. C. Haugen, J. Tao, and H. Li, Mol. Phys. 109, 435 (2011)], and the Chebyshev polynomial expansion potential [L. Busevica, I. Klincare, O. Nikolayeva, M. Tamanis, R. Ferber, V. V. Meshkov, E. A. Pazyuk, and A. V. Stolyarov, J. Chem. Phys. 134, 104307 (2011)]. In contrast with the expanded Morse oscillator potential determined in the original DPF analysis of Merritt et al. [Science 324, 1548 (2009)], both of these functions unambiguously support the existence of the v″ = 11 last vibrational levels which is bound by only ∼0.5 cm(-1), and they give equivalent, essentially exact predictions for this level when using the original data set which ended at v″ = 10. These empirical potentials predict an equilibrium distance of re = 2.445(5) Å and a well depth of D(e) = 934.9(0.4) cm(-1), values which agree (within the uncertainties) with the best ab initio estimates of 2.444(10) Å and 935(10) cm(-1), respectively [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)].

Organohelium Compounds: Structures, Stabilities and Chemical Bonding Analyses

This paper deals with the possibility of forming short and relatively strong carbon-helium bonds in small typical organic molecules through substitution of one or several H atoms by He(+). A structural and energetics study (based on high-level calculations) of this unusual bonding, as well as a topological characterization of the resulting cations, is undertaken. Stable species generally requires substitution of about half of the hydrogen atoms for formation. Under these conditions, the number of such species appears to be potentially unlimited. "True" C-He bonds exhibit equilibrium distances ranging from 1.327 (C2H2He2(2+)) to 1.129 Å (He2CO(2+)). The energies of neutral He releasing range from approximately 5 kcal mol(-1) [He2CO(2+), (Z)-C2H2He2(2+)] to 25 kcal mol(-1) (C2HHe3(3+)), but remain most frequently around 10 kcal mol(-1). However, most of He(+)-substituted hydrocarbons are metastable with respect to C-C cleavage, except derivatives of ethene. Atoms in molecules (AIM) and electron localization function (ELF) topological descriptors classify the C-He bond as a weak charge-shift interaction [S. Shaik, D. Danovich, B. Silvi, D. L. Lauvergnat, P. C. Hiberty, Chem. Eur. J. 2005, 11, 6358-6371] in agreement with a recent publication by Rzepa [S. H. Rzepa, Nat. Chem. 2010, 2, 390-393]. He2CO(2+) is the only investigated compound that presents a C-He bonding ELF basin, which indicates a non-negligible covalent contribution to the bond. Other modifications in the electronic structure, such as the breaking of the triple bond in ethyne derivatives or the loss of aromaticity in C6H3He3(3+), are also nicely revealed by the ELF topology.

The Cysteine-rich Region of Type VII Collagen Is a Cystine Knot with a New Topology

Collagens are a group of extracellular matrix proteins with essential functions for skin integrity. Anchoring fibrils are made of type VII collagen (Col7) and link different skin layers together: the basal lamina and the underlying connective tissue. Col7 has a central collagenous domain and two noncollagenous domains located at the N and C terminus (NC1 and NC2), respectively. A cysteine-rich region of hitherto unknown function is located at the transition of the NC1 domain to the collagenous domain. A synthetic model peptide of this region was investigated by CD and NMR spectroscopy. The peptide folds into a collagen triple helix, and the cysteine residues form disulfide bridges between the different strands. The eight cystine knot topologies that are characterized by exclusively intermolecular disulfide bridges have been analyzed by molecular modeling. Two cystine knots are energetically preferred; however, all eight disulfide bridge arrangements are essentially possible. This novel cystine knot is present in type IX collagen, too. The conserved motif of the cystine knot is CX3CP. The cystine knot is N-terminal to the collagen triple helix in both collagens and therefore probably impedes unfolding of the collagen triple helix from the N terminus.

Correlation Energies from the Two-Component Random Phase Approximation.

The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data.

Cα–H Carries Information of a Hydrogen Bond Involving the Geminal Hydroxyl Group: A Case Study with a Hydrogen-Bonded Complex of 1,1,1,3,3,3-Hexafluoro-2-propanol and Tertiary Amines

Experimental measurement of the contribution of H-bonding to intermolecular and intramolecular interactions that provide specificity to biological complex formation is an important aspect of macromolecular chemistry and structural biology. However, there are very few viable methods available to determine the energetic contribution of an individual hydrogen bond to binding and catalysis in biological systems. Therefore, the methods that use secondary deuterium isotope effects analyzed by NMR or equilibrium or kinetic isotope effect measurements are attractive ways to gain information on the H-bonding properties of an alcohol system, particularly in a biological environment. Here, we explore the anharmonic contribution to the C-H group when the O-H group of 1,1,1,3,3,3-hexafluoro-2-propanol (HFP) forms an intermolecular H-bond with the amines by quantum mechanical calculations and by experimentally measuring the H/D effect by NMR. Within the framework of density functional theory, ab initio calculations were carried out for HFP in its two different conformational states and their H-bonded complexes with tertiary amines to determine the (13)C chemical shielding, change in their vibrational equilibrium distances, and the deuterium isotope effect on (13)C2 (secondary carbon) of HFP upon formation of complexes with tertiary amines. When C2-OH was involved in hydrogen bond formation (O-H as hydrogen donor), it weakened the geminal C2-H bond; it was reflected in the NMR chemical shift, coupling constant, and the equilibrium distances of the C-H bond. The first derivative of nuclear shielding at C2 in HFP was -48.94 and -50.73 ppm Å(-1) for anti and gauche conformations, respectively. In the complex, the values were -50.28 and -50.76 ppm Å(-1), respectively. The C-H stretching frequency was lower than the free monomer, indicating enhanced anharmonicity in the C-H bond in the complex form. In chloroform, HFP formed a complex with the amine; δC2 was 69.107 ppm for HFP-triethylamine and 68.766 ppm for HFP-d2-triethylamine and the difference in chemical shift, the ΔδC2 was 341 ppb. The enhanced anharmonicity in the hydrogen-bonded complex resulted in a larger vibrational equilibrium distance in C-H/D bonds. An analysis with the Morse potential function indicated that the enhanced anharmonicity encountered in the bond was the origin of a larger isotope effect and the equilibrium distances. Change in vibrational equilibrium distance and the deuterium isotope effect, as observed in the complex, could be used as parameters in monitoring the strength of the H-bond in small model systems with promising application in biomacromolecules.

HYDRODYNAMIC INTERACTION OF TWO SPHERICAL BUBBLES RISING IN-LINE: A SEMI-ANALYTICAL APPROACH

A model is proposed to relate the flow structure in the wake behind a leading bubble with the hydrodynamic force acting on the trailing bubble rising in-line. The model is valid at separation distances between bubbles (s) within the same order of magnitude as their diameters (dB) (2.5 ≤ s/dB ≤ 14.5) and moderate-to-large particle Reynolds numbers (50 ≤ Re1 ≤ 300). An equation for the axial velocity profile in the wake of a spherical bubble was proposed in the form of an analytical approximation, but incorporating a theoretically reasoned artificial origin, which was fitted to numerical data. This equation, once substituted in a general hydrodynamic force model, resulted in a predictive equation explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. Moreover, the force experienced by the leading bubble due to the trailing bubble presence was obtained, and the theoretical equilibrium distances between the bubbles were calculated; good agreement with known behavior was achieved.

Comparative bonding analysis of N2 and P2 versus tetrahedral N4 and P4

The nature of the chemical bonds in E2 and tetrahedral E4 (E = N, P) has been analysed with the help of an energy decomposition method. The π bonds in P2 are not particularly weak. On the contrary, the contribution of P–P π bonding to the chemical bond in P2 is even higher than the contribution of N–N π bonding to the chemical bond in N2. The higher stability of P4 (T d) and the much lower stability of N4 (T d) with regard to the diatomic species come from the substantially larger weakening of the N–N σ-bonds compared with the P–P σ-bonds in the tetrahedral species. The sum of the six P–P σ-bond energies in P4 is higher than the sum of two σ- and four π-bonds in two P2, but the six N–N σ-bonds in N4 are weaker than two σ- and four π-bonds in two N2. The crucial factor that leads to the weak N–N bonds in N4, is the rather long N–N bonds which are 32.8 % longer than in N2. In contrast, the P–P bonds in P4 are only 16.2 % longer than in P2. Since the equilibrium distances in E2 and E4 are determined by Pauli repulsion, it can be concluded that the origin for the different stabilities of N4 and P4 relative to the diatomic molecules is the exchange repulsion. The nitrogen atoms encounter stronger Pauli repulsion, because the 2s and 2p valence orbitals have a similar radius while the 3s and 3p radii are more different.

Assessing the Performance of CASPT2 and DFT Methods for the Description of Long, Multicenter Bonding in Dimers between Radical Ions.

The performance of a wide variety of density functionals for the description of long, multicenter bonding in dimers between radical ions has been addressed in this work. Results on interaction energies and equilibrium distances have been evaluated through pure GGA and meta-GGA, hybrid, RSH, and double hybrid functionals. Grimme's dispersion corrections have also been assessed. All results are systematically analyzed and compared for the π-[TCNE]2(2-), π-[TTF]2(2+), π-[TCNB]2(2-), and π-[TCNP]2(2-) dimers. The DFT results are benchmarked against RASPT2 calculations based on large active spaces. It is shown that small active spaces do not quantitatively describe the interaction energy curves of these dimers. B97-D3(BJ) turns to be the functional that best reproduces the finest RASPT2 results, while PBE-D3(BJ), B3LYP-D3(BJ), and M06-L also provide satisfactory results.

The nature of the I⋯I interactions and a comparative study with the nature of the π⋯π interactions

The I⋯I interactions play an important role in molecular self-assembly. In the present study, the nature of the I⋯I interactions has been investigated and compared with the nature of the π⋯π interactions by using the I2 dimer and benzene dimer as the prototypes of these interactions. The CCSD(T) interaction energies in the complete basis set limit at the equilibrium distances are −1.51, −2.04, and −3.08kcal/mol for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer, respectively. These energy values are little different from the corresponding ones of the benzene dimer. In addition to accurate interaction energies, we have also performed symmetry adapted perturbation theory analyses for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer and benzene dimer. The dispersion interaction was found to be the major source of attraction in the sandwich and parallel-displaced configurations of the I2 dimer and benzene dimer. Different from the T-shaped configuration of the benzene dimer in which the dispersion interaction is still the major source of attraction, electrostatic, induction and dispersion interactions play equal role for the stabilization of the T-shaped configuration of the I2 dimer. On the other hand, potential energy curves for the sandwich, parallel-displaced, and T-shaped configurations of the I2 dimer were obtained employing different wave function and density functional theories with several large basis sets. It was noted that, for the T-shaped configuration of the I2 dimer, all the theory methods considered in this work cannot give comparable results to the CCSD(T) ones in the complete basis set limit. Relationships between the nature of the I⋯I and π⋯π interactions and the performance of theory methods were discussed.

Charge distribution of metallic single walled carbon nanotube–graphene junctions

We report numeric and analytic calculations of the electrostatic properties for armchair carbon nanotube–graphene junctions. Using a semi-empirical method we first demonstrate that the equilibrium distance between a carbon nanotube and a graphene sheet varies with respect to the diameter of the carbon nanotube. We find significantly reduced values compared to AB-stacked graphene sheets in graphite, while even smaller value is found for a fullerene C60 implying a dimensionality dependence of the equilibrium distance between graphene and the other sp2 carbon allotropes. Then, we use conformal mapping and a charge–dipole model to study the charge distribution of the carbon nanotube–graphene junctions in various configurations. We observe that the charges are accumulated/depleted at and near the vicinity of the junctions and that capped carbon nanotubes induce a significantly smaller charge concentration at their ends than the open-end nanotubes. We demonstrate that the carbon nanotube influence on the graphene sheet is limited to only few atomic rows. Such an influence strongly depends on the distance between carbon nanotube and the graphene sheet and scales with the carbon nanotube radius, while the potential difference does not modify the length over which the charge concentration is disturbed by the presence of the tube. By studying the potential landscape of carbon nanotube–graphene junctions, our work could be used as a starting point to model the charge carrier injection in these unconventional systems.

Decentralized Leader-Follower Flocking of Multiple Non-Holonomic Agents

In this paper, we study the cohesive flocking problem of multiple non-holonomic agents governed by extended second-order unicycle dynamics, such as robotic fish. Consider the system with only one leader. Combining the consensus algorithm and attraction/repulsion functions, a distributed flocking algorithm is presented for multiple robotic fish to complete the cohesive flocking task. According to LaSalle-Krasovskii invariance principle, the proposed algorithm enables followers to asymptotically track the leader's velocity and approach the equilibrium distances with their neighbors, provided that the initial interaction network among the followers is an undirected connected graph, and there exists at least one follower having a leader neighbor at the initial time. During the evolutionary process, the connectivity of the communication network can be preserved due to the effect of the potential function. Finally, a simulation example is given to verify the proposed theoretical analysis.

All-electron configuration interaction study on potential energy curves of low-lying excited states and spectroscopic properties of SiS

The 18 -S states correlated to the lowest dissociation (Si(3Pg)+S(3Pg)) limit are computed with high-level multireference configuration interaction (MRCI(SD)) approach through utilizing all-electron aug-cc-pwCVQZ-DK basis set. The scalar relativistic effect and the core-valence correlation effect of Si (2s22p6) and S (2s22p6) are taken into account. On the basis of calculated potential energy curves, the spectroscopic constants of the bound states are fitted, including equilibrium distance Re, adiabatic transition energies Te, harmonic vibrational frequencies e, anharmonic terms exe, and rotational constant Be. The electronic configurations at different bond lengths are given. The electronic dipole moments of 18 -S states are calculated, illuminating the influence of electronic configuration variation on electronic dipole moment. With the help of nonvanishing spin-orbit matrix elements including b3 and A1 as a function of the internuclear distance, the nearby state perturbations to b3 and A1 are discussed in detail. Finally, the transition dipole moments and Franck-Condon factors of A1X1+ and E1+X1+ transitions are obtained, and radiative lifetimes of five lowest vibrational levels of the two singlet excited states are evaluated.

Core structure and dissociation energetics of basal edge dislocation in α-Al2O3: A combined atomistic simulation and transmission electron microscopy analysis

Using large-scale molecular dynamics (MD) simulations, we investigate the energetics and local structures/stresses of partial dislocations, 1/3〈011¯0〉 and 1/3〈101¯0〉, dissociated from the 1/3〈112¯0〉 perfect basal edge dislocation in α-Al2O3. The validity of the model adopted in the simulation is confirmed by comparing with theoretical stress/strain distributions and with those experimentally obtained from a high-resolution transmission electron microscopy (HRTEM) observation. Partial dislocation pairs have a stable inter-core distance (∼2nm), which is also a phenomenon that is observed in the HRTEM experiments. The distance between the partials can be explained quantitatively by the balance between an elastic core–core repulsion and an effective attractive force against the extension of stacking faults (SFs). A comparison is made for two types of core structures of partial dislocations: a pair of partials with Al-terminated/O-terminated extra-half planes and that with Al-/Al-terminated ones. The overall tendency of the inter-core interaction and the equilibrium distances are the same in both cases, whereas the Al–O-terminated pair is slightly favourable in energy at the equilibrium distance. A residual shear stress on the SF plane is observed in the MD results, which can be attributed to local atomic structure in the SF.

Adhesion Analysis Considering van der Waals Force in a NanoSized Region Using the Boundary Element Method

Recently, micro- and nanomachines for microelectromechanical systems and the mechanism of bio-adhesive pads have attracted great interest. Nanoscale structures are affected by forces such as the van der Waals force, even though they are neglected in large-scale structures. In this paper, the van der Waals force is introduced to a boundary element method (BEM) program for analyzing adhesion in arbitrarily shaped bodies. The van der Waals force is described by a nonlinear function of the distance between two surfaces in close proximity, and the adhesion and repulsion forces vary greatly within the atom equilibrium distance. Therefore, it is difficult to obtain a solution for the simultaneous equation in the BEM. We propose a method to compute the body deformation and apply it to the adhesion between a cylinder and a flat, rigid substrate. The solution is compared with previously published theoretical results, and the validity of the algorithm for approaching the solution is demonstrated. Further calculations for the adhesive contact of softer and harder cylinders with a rigid substrate are conducted.

Block correlated second order perturbation theory with a generalized valence bond reference function

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Axial Equilibrium Distance and Positioning of Particles in a Laminar Tube Flow

AbstractParticle transport in a laminar tube flow at low Reynolds numbers leads to accumulation of particles at specific equilibrium radii. The equilibrium radius depends on the particle size. Small particles find their equilibrium radius near the wall and large particles near the tube axis. During their radial migration to the equilibrium position, the particles move in axial direction with the flow. In an experimental setup, the axial equilibrium distance is measurement for several tube Reynolds numbers. The axial equilibrium distance is the distance a particle migrates in the flow direction, until it reaches its radial equilibrium position. The results are compared with CFD‐simulations of single particle movement in a laminar tube flow.

Sunspot Group Development in High Temporal Resolution

The Solar and Heliospheric Obseratory/Michelson Doppler Imager--Debrecen Data (SDD) sunspot catalogue provides an opportunity to study the details and development of sunspot groups on a large statistical sample. The SDD data allow, in particular, the differential study of the leading and following parts with a temporal resolution of 1.5 hours. In this study, we analyse the equilibrium distance of sunspot groups as well as the evolution of this distance over the lifetime of the groups and the shifts in longitude associated with these groups. We also study the asymmetry between the compactness of the leading and following parts, as well as the time-profiles for the development of the area of sunspot groups. A logarithmic relationship has been found between the total area and the distance of leading-following parts of active regions (ARs) at the time of their maximum area. In the developing phase the leading part moves forward; this is more noticeable in larger ARs. The leading part has a higher growth rate than the trailing part in most cases in the developing phase. The growth rates of the sunspot groups depend linearly on their maximum total umbral area. There is an asymmetry in compactness: the number of spots tends to be smaller, while their mean area is larger in the leading part at the maximum phase.