Geometry optimization of periodic systems using internal coordinates

Understanding Structure and Bonding of Multilayered Metal-Organic Nanostructures

For organic and hybrid electronic devices, the physicochemical properties of the contained interfaces play a dominant role. To disentangle the various interactions occurring at such heterointerfaces, we here model a complex, yet prototypical, three-component system consisting of a Cu-phthalocyanine (CuPc) film on a 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) monolayer adsorbed on Ag(111). The two encountered interfaces are similar, as in both cases there would be no bonding without van der Waals interactions. Still, they are also distinctly different, as only at the Ag(111)-PTCDA interface do massive charge-rearrangements occur. Using recently developed theoretical tools, we show that it has become possible to provide atomistic insight into the physical and chemical processes in this comparatively complex nanostructure distinguishing between interactions involving local rearrangements of the charge density and long-range van der Waals attraction.

Temperature-dependent ideal strength and stacking fault energy of fcc Ni: a first-principles study of shear deformation

Variations of energy, stress, and magnetic moment of fcc Ni as a response to shear deformation and the associated ideal shear strength (τ(IS)), intrinsic (γ(SF)) and unstable (γ(US)) stacking fault energies have been studied in terms of first-principles calculations under both the alias and affine shear regimes within the {111} slip plane along the <112> and <110> directions. It is found that (i) the intrinsic stacking fault energy γ(SF) is nearly independent of the shear deformation regimes used, albeit a slightly smaller value is predicted by pure shear (with relaxation) compared to the one from simple shear (without relaxation); (ii) the minimum ideal shear strength τ(IS) is obtained by pure alias shear of {111}<112>; and (iii) the dissociation of the 1/2[110] dislocation into two partial Shockley dislocations (1/6[211] + 1/6[121]) is observed under pure alias shear of {111}<110>. Based on the quasiharmonic approach from first-principles phonon calculations, the predicted γ(SF) has been extended to finite temperatures. In particular, using a proposed quasistatic approach on the basis of the predicted volume versus temperature relation, the temperature dependence of τ(IS) is also obtained. Both the γ(SF) and the τ(IS) of fcc Ni decrease with increasing temperature. The computed ideal shear strengths as well as the intrinsic and unstable stacking fault energies are in favorable accord with experiments and other predictions in the literature.

Ab initio study of structure and interconversion of native cellulose phases

Dispersion-interaction corrected DFT simulations are performed to study the structure of two allomorphs of native cellulose I. Good agreement between theoretical and experimental data is achieved. Two H-bond patterns, previously identified experimentally, are examined for both allomorphs. The transition mechanism for the conversion between the phase I(α) and I(β) is studied by means of constrained relaxations. New metastable intermediate phase occurring on the I(α) → I(β) route is identified, and the corresponding structural data are reported.

Improved description of the structure of molecular and layered crystals: ab initio DFT calculations with van der Waals corrections

The implementation of technique for full structural optimizations of complex periodic systems in the DFT-PAW package VASP, including the volume and shape of the unit cell and the internal coordinates of the atoms, together with a correction that allows an appropriate modeling of London dispersion forces, as given by the DFT-D2 approach of Grimme [Grimme, S. J. Comp. Chem. 2006, 27, 1787], is reported. Dispersion corrections are calculated not only for the forces acting on the atoms, but also for the stresses on the unit cell. This permits a simultaneous optimization of all degrees of freedom. Benchmark results on a series of prototype systems are presented and compared to results obtained by other methods and experimental data. It is demonstrated that the computationally inexpensive DFT-D2 scheme yields reasonable predictions for the structure, bulk moduli, and cohesive energies of weakly bonded materials.

Electronic structure of pyridine-based SAMs on flat Au(111) surfaces: extended charge rearrangements and Fermi level pinning

Density functional theory calculations are used to investigate the electronic structure of pyridine-based self-assembled monolayers (SAMs) on an Au(111) surface. We find that, when using pyridine docking groups, the bonding-induced charge rearrangements are frequently found to extend well onto the molecular backbone. This is in contrast to previous observations for the chemisorption of other SAMs, e.g., organic thiolates on gold, and can be explained by a pinning of the lowest unoccupied states of the SAM at the metal Fermi-level. The details of the pinning process, especially the parts of the molecules most affected by the charge rearrangements, strongly depend on the length of the molecular backbone and the tail-group substituent. We also mention methodological shortcomings of conventional density functional theory that can impact the quantitative details regarding the circumstances under which pinning occurs and highlight a number of peculiarities associated with bond dipoles that arise from Fermi-level pinning.

The electronic structure of mixed self-assembled monolayers

The electronic structure of mixed self-assembled monolayers (SAMs) on Au(111) surfaces is modeled using slab-type density-functional theory calculations. The studied molecules have a dipolar character induced by polar and electron donating or accepting tail-group substituents. The resulting electronic structure of mixed layers is found to differ qualitatively from a simple superposition of those of the respective pure layers. Specifically, the positions of the frontier electronic states are shifted relative to the metal Fermi level, with the sign and magnitude of that shift depending on the dipole moment of the molecules and the mixing ratio in the film. This appears counterintuitive considering previous investigations, in which it has been shown that, for densely packed layers, tail-group substituents have no impact on the interfacial energy-level alignment. The seeming contradiction can be lifted by considering the local electrostatic interactions within the films in both mixed and homogeneous monolayers. Beyond that, we show that mixed SAMs provide an efficient tool for continuously tuning substrate work functions over a range that far exceeds that accessible by merely changing the coverage of homogeneous layers, with the net effect depending linearly on the mixing ratio in agreement with recent experimental findings.

Ab Initio Investigation of Structure and Cohesive Energy of Crystalline Urea

The structure and cohesive energy of crystalline urea have been investigated at the ab initio level of calculation. The performance of different Hamiltonians in dealing with a hydrogen-bonded molecular crystal as crystalline urea is assessed. Detailed calculations carried out by adopting both HF and some of the most popular DFT methods in solid-state chemistry are reported. Local, gradient-corrected, and hybrid functionals have been adopted: SVWN, PW91, PBE, B3LYP, and PBE0. First, a 6-31G(d,p) basis set has been adopted, and then the basis set dependence of computed results has been investigated at the B3LYP level. All calculations were carried out by using a development version of the periodic ab initio code CRYSTAL06, which allows full optimization of lattice parameters and atomic coordinates. With the 6-31G(d,p) basis set, structural features are well reproduced by hybrid methods and GGA. LDA gives lattice parameters and hydrogen-bond distances that are too small relative to experiment, while at the HF level the opposite trend is observed. Results show that hybrid methods are more accurate than HF and both LDA and GGA functionals, with a trend in the computed properties similar to that of hydrogen-bonded molecular complexes. When BSSE and ZPE are taken into account, all methods, except LDA, give computed cohesive energies that are underestimated with respect to the experimental sublimation enthalpy. Dispersion energy, not properly taken into account by DFT methods, plays a crucial role. Such a deficiency also affects dramatically the computed crystalline structure, especially when large basis sets are adopted. We show that this is an artifact due to the BSSE. Indeed, with small basis sets the BSSE gives an extra-binding that compensates for the missing dispersion forces, thus yielding structures in fortuitous agreement with experiment.

Energy gradients with respect to atomic positions and cell parameters for the Kohn-Sham density-functional theory at the Γ point

The application of theoretical methods based on density-functional theory is known to provide atomic and cell parameters in very good agreement with experimental values. Recently, construction of the exact Hartree-Fock exchange gradients with respect to atomic positions and cell parameters within the Gamma-point approximation has been introduced. In this article, the formalism is extended to the evaluation of analytical Gamma-point density-functional atomic and cell gradients. The infinite Coulomb summation is solved with an effective periodic summation of multipole tensors. While the evaluation of Coulomb and exchange-correlation gradients with respect to atomic positions are similar to those in the gas phase limit, the gradients with respect to cell parameters needs to be treated with some care. The derivative of the periodic multipole interaction tensor needs to be carefully handled in both direct and reciprocal space and the exchange-correlation energy derivative leads to a surface term that has its origin in derivatives of the integration limits that depend on the cell. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm to optimize one-dimensional and three-dimensional periodic systems at the density-functional theory and hybrid Hartree-Fock/density-functional theory levels. We also report the full relaxation of forsterite supercells at the B3LYP level of theory.

Exchange energy gradients with respect to atomic positions and cell parameters within the Hartree-Fock Γ-point approximation

Recently, linear scaling construction of the periodic exact Hartree-Fock exchange matrix within the Gamma-point approximation has been introduced [J. Chem. Phys. 122, 124105 (2005)]. In this article, a formalism for evaluation of analytical Hartree-Fock exchange energy gradients with respect to atomic positions and cell parameters at the Gamma-point approximation is presented. While the evaluation of exchange gradients with respect to atomic positions is similar to those in the gas phase limit, the gradients with respect to cell parameters involve the accumulation of atomic gradients multiplied by appropriate factors and a modified electron repulsion integral (ERI). This latter integral arises from use of the minimum image convention in the definition of the Gamma-point Hartree-Fock approximation. We demonstrate how this new ERI can be computed with the help of a modified vertical recurrence relation in the frame of the Obara-Saika and Head-Gordon-Pople algorithm. As an illustration, the analytical gradients have been used in conjunction with the QUICCA algorithm [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] to optimize periodic systems at the Hartree-Fock level of theory.

Geometry optimization of crystals by the quasi-independent curvilinear coordinate approximation

The quasi-independent curvilinear coordinate approximation (QUICCA) method [K. Nemeth and M. Challacombe, J. Chem. Phys. 121, 2877 (2004)] is extended to the optimization of crystal structures. We demonstrate that QUICCA is valid under periodic boundary conditions, enabling simultaneous relaxation of the lattice and atomic coordinates, as illustrated by tight optimization of polyethylene, hexagonal boron nitride, a (10,0) carbon nanotube, hexagonal ice, quartz, and sulfur at the Gamma-point RPBE/STO-3G level of theory.