Global Minimum Determination of the Born-Oppenheimer Surface within Density Functional Theory

Abstract

We present a novel method, which we shall refer to as the dual minima hopping method (DMHM), that allows us to find the global minimum of the potential energy surface (PES) within density functional theory (DFT) for systems where a fast but less accurate calculation of the PES is possible. This method can rapidly find the ground state configuration of clusters and other complex systems with present day computer power by performing a systematic search. We apply the new method to silicon clusters. Even though these systems have already been extensively studied by other methods, we find new configurations for Si16, Si18 and Si19 that are lower in energy than those found previously.Determining the structure of a molecule, cluster or crystal is one of the most fundamental and important tasks in solid state physics and chemistry. Practically all physical properties of a system depend on its structure. The structural configurations of a system are determined by the Born-Oppenheimer PES, which gives the energy of a system as a function of its atomic coordinates. Minima of the PES give stable configurations. The global minimum gives the ground state configuration. At low enough temperature the system will be found in this global minimum structure assuming that this structure is kinetically accessible. Since the zero point energy of different structures varies negligibly, the determination of the ground state structure is equivalent to the mathematical problem of finding the global minimum of the PES.It is well established that the PES of a condensed matter system can be calculated with good accuracy within DFT. Nevertheless, DFT methods have not been used up to now as a standard tool in algorithms that attempt to determine the ground state of complex systems because most algorithms for the determination of the global minimum require an enormous number of evaluations of the PES. Since each evaluation requires a full electronic structure calculation, these algorithms are computationally too demanding within the full DFT framework. A systematic search for the global minimum is however possible with cheaper methods such as tight binding and force field methods.In summary, with present methods one has either the choice of using methods with a limited power of predictability or of doing a constrained search for the global minimum. In a constrained search one fixes some atomic positions or imposes some structural motifs, but experience shows that the global minimum is often missed in this way. To overcome this dilemma several researchers have adopted an approach where one first effectuates a systematic search with a method that allows for a fast but inaccurate calculation of the PES to obtain some candidate structures. Which of the candidate structures is lowest in energy is determined in a second step by DFT calculations. As we shall show later this approach is generally not applicable.Other researches have combined systematic search algorithms with DFT methods, but their algorithms required too many DFT calculations to be com...

Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si15 to Si20

“…Si 16 Goedecker et al 8 showed that 16ttp-1 has the lowest energy whereas 16ss-1 is the second in the energy order on the basis of PWP-DFT calculations with the PBE functional. However, on basis of all-electron DFT calculations with both B3LYP and PBE1PBE hybrid functionals and the 6-311G ͑2d͒ basis set, we found that 16ss-1 is always lower in energy than 16ttp-1.…”

“…The 16bilayer isomer was previously predicted to be the global minimum by Ho et al, 3 and its structure can be viewed as a network of eight parallel silicon dimers. The 16bilayer-1r, which was reported by Goedecker et al as the third lowestenergy isomer, 8 can be constructed by rotating three pairs of silicon dimers of 16bilayer-1 by 90°at the top. In addition, we display a cagelike isomer of Si 16 named 16cage-1.…”

“…Recently, Goedecker et al 8 reported a new candidate for the global minimum of Si 16 as well as for Si 19 , based on a novel minima-hopping method 9 and total-energy calculation using the PWP-DFT with the PBE functional implemented in the CPMD program. More interestingly, they found that these new structures of Si 16 and Si 19 all contain the TTP Si 9 motif rather than the six/six Si 6 /Si 6 motif.…”

High temperature superconductivity in sulfur and selenium hydrides at high pressure

“…And the experimental evidence was immediately supported by calculations [32,[35][36][37]39,45,46]. In this work [47] we want study in detail the S-H phases with state of the art ab-initio material search minima hopping method (MHM) [48][49][50] and compute the superconducting properties with the completely parameter-free Density Functional Theory for Superconductors (SCDFT) [51]. At the same time we also extend the analysis to the Se-H system, predicting a fairly similar phase diagram and comparable superconducting properties.…”

The Geometric Structure of Silver‐Doped Silicon Clusters

“…[1,2] Silicon clusters have been extensively investigated experimentally [3][4][5][6][7] and theoretically. [8][9][10][11][12][13][14][15] Contrary to the isolobal carbon, silicon favors sp 3 hybridization rather than sp 2 hybridization, which leads to rather asymmetric and reactive structures for pure silicon clusters and makes the formation of cage-like structures unstable. [16] One possible solution to overcome this deficiency is to add transition metal dopant atoms to the silicon clusters, which is known to induce the formation of stable and unreactive cage-like structures.…”