Pd8 Cluster: Too Small to Melt? A BOMD Study.

The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.

Self-Consistent Auxiliary Density Perturbation Theory.

The working equations for the extension of auxiliary density perturbation theory (ADPT) to hybrid functionals, employing the variational fitting of the Fock potential, are derived. The response equations in the resulting self-consistent ADPT (SC-ADPT) are solved iteratively with an adapted Eirola-Nevanlinna algorithm. As a result, a memory and CPU time efficient implementation of perturbation theory free of four-center electron repulsion integrals (ERIs) is obtained. Our validation calculations of SC-ADPT static and dynamic polarizabilities show quantitative agreement with corresponding coupled perturbed Hartree-Fock and Kohn-Sham results employing four-center ERIs. The comparison of SC-ADPT hybrid functional polarizabilities with coupled cluster reference calculations yield semiquantitative agreement. The presented systematic study of the dynamic polarizabilities of oligothiophenes shows that hybrid functionals can overcome the pathological misplacement of excitation poles by the local density and generalized gradient approximations. Good agreement with experimental dynamic polarizabilities for all studied oligothiophenes is achieved with range-separated hybrid functionals in the framework of SC-ADPT.

On the forbidden graphene's ZO (out-of-plane optic) phononic band-analog vibrational modes in fullerenes.

The study of nanostructures' vibrational properties is at the core of nanoscience research. They are known to represent a fingerprint of the system as well as to hint the underlying nature of chemical bonds. In this work, we focus on addressing how the vibrational density of states (VDOS) of the carbon fullerene family (Cn: n = 20 → 720 atoms) evolves from the molecular to the bulk material (graphene) behavior using density functional theory. We find that the fullerene's VDOS smoothly converges to the graphene characteristic line-shape, with the only noticeable discrepancy in the frequency range of the out-of-plane optic (ZO) phonon band. From a comparison of both systems we obtain as main results that: (1) The pentagonal faces in the fullerenes impede the existence of the analog of the high frequency graphene's ZO phonons, (2) which in the context of phonons could be interpreted as a compression (by 43%) of the ZO phonon band by decreasing its maximum allowed radial-optic vibration frequency. And 3) as a result, the deviation of fullerene's VDOS relative to graphene may hold important thermodynamical implications, such as larger heat capacities compared to graphene at room-temperature. These results provide insights that can be extrapolated to other nanostructures containing pentagonal rings or pentagonal defects.

Variational Density Fitting with a Krylov Subspace Method.

In this work, we present the implementation of a variational density fitting methodology that uses iterative linear algebra for solving the associated system of linear equations. It is well known that most difficulties with this system arise from the fact that the coefficient matrix is in general ill-conditioned and, due to finite precision round-off errors, it may not be positive definite. The dimensionality, given by the number of auxiliary functions, also poses a challenge in terms of memory and time demand since the coefficient matrix is dense. The methodology presented is based on a preconditioned Krylov subspace method able to deal with indefinite ill-conditioned equation systems. To assess its potential, it has been combined with double asymptotic electron repulsion integral expansions as implemented in the deMon2k package. A numerical study on a set of problems with up to 130,000 auxiliary functions shows its effectiveness to alleviate the abovementioned problematic. A comparison with the default methodology used in deMon2k based on a truncated eigenvalue decomposition of the coefficient matrix indicates that the proposed method exhibits excellent robustness and scalability when implemented in a parallel setting.