Towards the development of wavefunction-based methods for materials modeling; Ali Alavi, Department of Chemistry, Trinity College, University of Cambridge, United Kingdom

We review some recent progress in using Monte Carlo methods in combination with quantum chemical methods to solve to a high degree of accuracy the many-electron Schrodinger equation, both in the molecular context as well as periodic boundary conditions. At the heart of the methods is FCIQMC [1,2,3], which simulates an exact stochastic representation of the FCI wavefunction of a physical system expressed in a finite basis. The sampled FCI wavefunction can be used to compute the 1- and 2-electron reduced density matrix, from which a great many physical properties can be extracted. In particular, these  can be used to compute a perturbative basis-set correction [3], which very accurately accounts for the basis-set error arising from the use of finite basis sets. We have recently extended this method to periodic systems [4], and results will be shown in this regard. Finally, we will review recent progress on alleviating the time-step bottleneck of FCIQMC, opening the possibility to simulate substantially larger systems than currently possible.


[1] G.H. Booth, A.J.W. Thom and Ali Alavi, J. Chem. Phys., 131 , 054106, (2009).
[2] Deidre Cleland, G.H. Booth, and Ali Alavi, J. Chem. Phys., 132, 041103, (2010).
[3] George H. Booth, Andreas Grueneis, Georg Kresse, and Ali Alavi, Nature , 493 365-370, (2013).
[4] G.H. Booth, D.M. Cleland, Ali Alavi, David Tew, J. Chem. Phys., 137, 164112, (2012).
[5] A. Grueneis, JJ Shepherd, A. Alavi, D.P. Tew, G.H.Booth, J. Chem. Phys, 139, 084112 (2013).

Nuclear quantum effects in ab initio simulations using colored noise and i-PI; Michele Ceriotti (EPFL)

The quantum nature of light nuclei plays a very important role in determining quantitatively the behaviour of hydrogen-containing materials. Conventional techniques to include nuclear quantum effects in atomistic simulations are computationally demanding and cumbersome to implement, which has limited their use in combination with accurate first-principles determination of the inter-atomic forces. Here I will discuss how these problems may be alleviated by using correlated Langevin dynamics to accelerate the convergence of observables to their quantum mechanical value. The implementation burden can also be greatly reduced by using i-PI, a Python interface that can be easily interfaced to any electronic structure code, to which the evaluation of forces on (classical) nuclear configurations is delegated. I will start by briefly describing the theoretical foundations of generalized Langevin equation thermostats, and their combination with path integral molecular dynamics. I will then describe the philosophy and the discuss practical usage of i-PI in association with first-principles packages such as quantum Espresso, CP2K, FHI-AIMS or CPMD. Finally, I will present a few examples, including the ab initio determination of the liquid-vapor isotope fractionation in water, that provides a stringent test of the accuracy of different density functionals for the evaluation of nuclear quantum effects.

Accelerating quantum transport simulations on massively parallel computing architectures; Mauro Calderara, Sacha Brück, Pierre Ferry, Mathieu Luisier (ETH Zurich)

The continuous reduction of the transistor size and the increase of their count per integrated circuit have both contributed to a significant improvement of portable electronic devices such as laptops, cell phones, or digital camera. As a consequence of this miniaturization process, the dimensions of the currently manufactured transistors do not exceed a couple of nanometers, their active region is composed of a countable number of atoms, and quantum mechanical effects have started to strongly influence their behavior. To accurately predict the characteristics of not-yet-fabricated nano-transistors, there is a strong need for simulation approaches that simultaneously capture their material and transport properties at a quantum mechanical level.

Density-functional theory (DFT) represents the most accurate method to satisfy this demand, but its computational burden usually restricts its application to small atomic systems. Empirical models such as tight-binding (TB) allow for the simulation of larger structures and the inclusion of complex scattering mechanisms but they lack predictability when surface effects become important or when new material combinations should be investigated. Although ab-initio and empirical quantum transport (QT) approaches have different domains of application, they both need large computational resources to efficiently run and can therefore benefit from massively parallel computing architectures.

To simulate electron transport through a nanostructure, the Schroedinger equation must be solved with open boundary conditions (OBCs) for different electron energies that are independent in the ballistic case but tightly coupled in the presence of electron-phonon scattering for example. In tight-binding computing the OBCs is facilitated by the small bandwidth of the Hamiltonian, shifting the main computational challenge to the solution of the Schroedinger equation, either in a so-called Wave Function (WF) formalism[1] or in the well-known Non-equilibrium Green's Function (NEGF) framework. In DFT transport calculations the OBCs induce the highest computational costs as the non-hermitian generalized eigenvalue problems associated with them are non-trivial to parallelize and generally outweigh the solution of the Schroedinger equation in terms of computational cost. The highly parallel FEAST algorithm[2] is very well-suited to fulfill this task.

As key results we will present DFT- and TB-based quantum transport simulations of realistic nano-devices as well as algorithmic innovations leveraging graphical processing units (GPUs). A single computer aided design tool will be used for that purpose. Combined with the CP2K[3] package, it can perform ab-initio transport simulations of nanowire transistors. In standalone configuration, it can treat a wide range of nanostructures at the tight-binding level.

The Cray XC30 Piz Daint at CSCS has been chosen as benchmark platform. We will show that on this system, the ballistic simulation of large nanowire and ultra-thin-body transistors expressed in a TB basis can be accelerated by a factor of 2.5 when the 8 cores per node of Piz Daint are assisted with one GPU. With electron-phonon scattering, speed ups larger than 40 can be reached when comparing 1 CPU with 1 GPU in the NEGF formalism. In the DFT case, a supercomputer like Piz Daint enables quantum transport simulations of nanowires with more than 10'000 atoms. Furthermore, due to the extremely good scalability of the FEAST algorithm, up to 128 threads or 2 GPUs can be assigned to the same energy point. Knowing that a typical device simulation includes more than 1000 such points, it appears that one single DFT-based QT run has the potential to scale up to the full dimensions of Piz Daint.

[1] M. Luisier et al., Phys. Rev. B 74, 205323 (2006). [2] E. Polizzi, Phys. Rev. B 79, 115112 (2009). [3] J. VandeVondele et al., Comput. Phys. Commun. 167, 103 (2005).

Enabling First Principles Simulations at the MP2 and RPA Level: An Efficient and Massively Parallel Algorithm Based on the Resolution-of-Identity Gaussian and Plane Waves Approach; Mauro Del Ben, Jurg Hutter (Department of Chemistry, University of Zurich), Joost VandeVondele (Department of Materials, ETH Zurich)

Density Functional Theory (DFT) has become the most widely used quantum mechanical tool in chemistry and physics for predicting properties of materials ranging from molecules to condensed phase systems. However, current approximate DFT still suffers from many flaws and the quest for finding more accurate functional is still ongoing. In this respect, the second-order M\o{}ller-Plesset perturbation theory (MP2) and the Random Phase Approximation (RPA), are increasingly popular post-Kohn-Sham electronic structure methods. Both MP2 and RPA display many appealing features such as the capability to describe covalent, ionic, hydrogen-bond and dispersion interactions accurately and from first principles. On the other hand, these advantages come at a computational cost that is significantly higher than traditional DFT. On this basis, the development of efficient algorithms, capable to exploit the performance of the latest supercomputers, is of prime interest in order to extend the applicability of these methods to larger and more realistic systems. Recently we have developed a novel algorithm for MP2 and RPA correlation energies of finite and extended systems based on a hybrid Gaussian and Plane Waves (GPW) approach with the resolution-of-identity approximation (RI). The key aspect of the method relies in the dual representation of the RI fitting densities in term of Gaussian and Plane Waves auxiliary functions, leading to a simplified treatment of the Coulomb interactions that is particularly efficient in the condensed phase. The RI approximation allows to speed up the MP2 energy calculations by a factor 10 to 15 compared to the canonical implementation, but still requiring $O(N^5)$ operations. On the other hand, in the RPA case, the combination of RI and imaginary frequency integration reduces the computational effort from $O(N^6)$ to $O(N^4 \log N)$. Our implementation has low memory requirements and displays excellent parallel scalability up to tens thousands of processes. Furthermore, the computationally more demanding parts, that is the $O(N^5)$ and $O(N^4)$ scaling steps respectively for MP2 and RPA, can be accelerated by employing graphics processing units (GPU) showing, for large systems, a gain of more than a factor two compared to the standard only CPU case. In this way, RI-MP2 and RI-RPA calculations for condensed phase systems containing hundreds of atoms and thousands of basis functions can be performed within minutes employing few hundreds hybrid nodes. This has allowed us to use these high level electronic structure methods for performing first principle simulations of bulk liquid water under ambient conditions.

References: - Del Ben, M.; Hutter, J.; VandeVondele J.; Electron correlation in the condensed phase from a Resolution of Identity approach based on the Gaussian and Plane Waves scheme. J. Chem. Theory Comput. 2013, 9, 2654 - Del Ben, M.; Schonherr, M.; Hutter, J.; VandeVondele, J.; Bulk liquid water at ambient temperature and pressure from MP2 theory. J. Phys. Chem. Lett. 2013, 4, 3753

SIESTA-PEXSI for large scale electronic structure calculations; Georg Huhs (BSC), Alberto Garcia (ICMAB-CSIC),  Chao Yang (LBNL)

For many demanding problems of material science the accuracy of first principle methods is needed. One of the most successful methods in this field is Density Functional Theory (DFT). Despite its success, it suffers from a limitation of the problem size it can be applied to, due to the O(N^3) scaling of the computational cost of the eigensolver needed, a problem which can not be overcome with increasing computing power alone.

The recently developed Pole EXpansion and Selected Inversion (PEXSI) algorithm is an alternative to the eigenpair computation. If sparse Hamiltonian and overlap matrices are used, it reduces the computational complexity to O(N^2) for 3D systems, and even further to O(N^1.5) for quasi-2D systems, and to O(N) for quasi-1D systems. Since there are no additional simplifications or assumptions involved, this method is accurate and generally applicable, also for metals and semi-metals. Additionally the structure of the algorithm allows parallelization on several levels, so that even over 100,000 cores can be used.

SIESTA is a widely used DFT code featuring sparse matrices due to its atomic orbital basis. PEXSI has been implemented into SIESTA and tested for various types and sizes of systems.

In this talk we will show, how SIESTA-PEXSI extends the range of physical problems accessible to simulation, its accuracy, and its potential for substantially improving the usage of modern high performance computing facilities.

Computational discovery of new structures using the minima hopping method; Stefan Goedecker (University of Basel)

Theoretical structure prediction methods can find a huge number of possible low energy structures of materials. I will present some basic principles for locating them efficiently and show how these principles are exploited in the minima hopping method. I will next survey some of our applications to various materials. I will present our studies of several hydrogen storage materials for which we found numerous hitherto unknown structures, computer generated silicon allotropes that have promising applications for photovoltaic applications and summarize our search for stable fullerene like structures beyond carbon. I will also address the question of whether theoretically found materials can be synthesized in practice and single out features of the potential energy landscape that facilitate the synthesis.

Engineering polar discontinuities in two-dimensional honeycomb lattices; Marco Gibertini, Giovanni Pizzi, Nicola Marzari (EPFL)

The unprecedented and fascinating phenomena taking place at oxide interfaces such as LaAlO3/SrTiO3 have recently triggered the search for their two-dimensional analogues. In this respect, honeycomb lattices seem to offer a rich playground, thanks to their versatility and the extensive on-going experimental efforts in graphene and related materials. Here we would like to emphasize, with the help of atomistic first-principles simulations, how to achieve polar discontinuities across interfaces between honeycomb lattices, elucidating the key physical processes that occur and their possible practical applications.

Quantum Mechanics/Machine Learning for chemically accurate high-throughput screening of thermo and quantum chemical properties of organic molecules; Raghunathan Ramakrishnan, Matthias Rupp, O. Anatole von Lilienfeld (Department of Chemistry, University of Basel) Pavlo O. Dral (Max Planck Institute for Coal Research, Germany)

Chemically accurate, large-scale exploration of molecular space is limited by the computational cost of quantum chemistry methods. We introduce a composite machine learning (ML) strategy for rapid prediction of corrections to routinely employed approximate quantum mechanical (QM) methods. After training, chemically accurate predictions of molecular thermochemical properties of new molecules are possible — with speed-ups of several orders of magnitude. We demonstrate the validity of this QM/ML approach by reproducing enthalpies and free energies of atomization calculated with density functional theory and quantum composite methods for over 130,000 organic molecules and for 6,095 constitutional isomers of C7H10O2 , respectively. QM/ML also predicts electron correlation energies in post Hartree-Fock methods with similar speed-ups and accuracies. We have successfully applied QM/ML to the high-throughput screening of over 10,000 stable diastereomers of C7 H10 O2 to identify the molecular pairs with maximal predicted enthalpy, entropy, and free energy of reaction at G4MP2 level of theory.

A combined classical and first-principles study to the modeling of resistance drift in phase-change materials; Federico Zipoli, Alessandro Curioni (IBM Research - Zurich)

Phase-change materials (PCM) based on chalcogenide alloys are considered very promising for memory storage applications. These materials are interesting because they undergo fast and reversible transitions between the amorphous and crystalline phases upon heating and cooling. These two phases have different electrical resistivities, which can be used to store and read the information. To render PCM-based devices competitive with flash memories, the amount of data that can be stored per unit of volume must be increased by setting more than two resistance values in the same cell. Unfortunately, the main limitation incurred hereby is data corruption caused by a change in resistivity of the amorphous phase on a timescale that is too short for a practical storage application. This limitation becomes even more relevant when trying to store more resistance values. Therefore, understanding the cause of the resistivity drift is a key step forward towards plan solutions to increase the storage density. We present a theoretical investigation of the amorphous phase of GeTe (a-GeTe), a prototypical PCM material currently being explored for memory applications. The goal is to investigate whether changes in resistivity are associated with a reorganization of the bond network in the amorphous phase or with the evolution of specific defects formed during the relatively fast quenching from the melt in the writing cycle. Our approach was to generate well annealed a-GeTe structures via classical molecular-dynamics (MD) simulations and then to characterize these structures via density-functional-theory calculations using the HSE hybrid functional. We used our classical Tersoff-based potential for classical MD simulations [New. J. of Phys. 15, 123006 (2013)]. The first-principles analysis shows that most of the Kohn-Sham states localized in the band gap are produced by defects consisting in groups of Ge atoms in which at least a Ge atom has to have a coordination that differs from that of the crystalline phase: three bonds and one lone pair. The large number of structures analyzed allows to estimate the statistic of defects. We correlate the topology of the bond network and the conductivity. We propose that, over time, a change in resistivity is produced by both consumption of these defects formed during the fast quenching and ordering of the bond network by removal of stretched bonds. Our model shows that this reduction results from a slow evolution of the bond network towards structures having a first-neighbor topology more similar to that of the crystalline phase. To support our model, we use first-principles Car-Parrinello MD simulations to study the evolution of a prototypical defect into a lower energy configuration which results in a structure with a larger gap.

Epitaxial strain-induced point-defect formation and ordering in oxides; Ulrich Aschauer, Nicola A. Spaldin (Materials Theory, ETH Zurich)

Using density functional theory calculations we recently established the existence of a strong coupling between epitaxial strain and the formation energy of oxygen vacancies in CaMnO$_3$ (PRB 88, 054111, 2013). Here we investigate the generality of this concept for other oxides and the effect of strain on the formation of cation vacancies. The response of the defect profile generally follows the behaviour expected from chemical expansion arguments but material specific deviations exist under both tensile and compressive strain. We will discuss the implications of our findings in the context of using epitaxial-strain to engineer multiferroic materials.

Linear Scaling Electronic Structure Theory; Ole Schütt, Jinwoong Cha, Samuel Andermatt, Florian Schiffmann, Urban Borstnik, Juerg Hutter, Joost VandeVondele (ETH Zürich)

In materials science, atomistic models must often capture features that are several nanometers in size. If the electronic structure is required to reliably describe the properties of such systems, linear scaling electronic structure approaches must be adopted to make computations feasible. In particular, finding orthonormal single particle orbitals must be avoided, and the density matrix of the system must be constructed in a way that avoids cubically scaling techniques, such as diagonalization. Fortunately, various techniques exist to exploit the nearsightedness of nature, and the quantities of interest, in particular the Hamiltonian and density matrices, can be represented and computed in a sparse form. With the high performance implementation of such linear scaling methods in CP2K, calculations, including molecular dynamics, on 10'000s of atoms have become easily feasible. The core operation employed by these methods is sparse matrix matrix multiplication. To perform this operation efficiently on massively parallel and hybrid computer architectures, a dedicated sparse matrix library, named DBCSR, has been developed. This library exploits multiple levels of parallelism, such as MPI, OpenMP and CUDA, and is based on kernels obtained using auto-tuning techniques. Results obtained of Europe's largest supercomputer, Piz Daint, will be presented.

Massively Parallel Hartree-Fock Exact Exchange Ab Initio Molecular Dynamics Simulations; Valery Weber, Costas Bekas, Teodoro Laino, Alessandro Curioni (IBM Research - Zurich)

We present a novel parallelization scheme for a highly efficient evaluation of the Hartree–Fock exact exchange (HFX) in ab initio molecular dynamics simulations, specifically tailored for condensed phase simulations. Our developments allow one to achieve the necessary accuracy or the evaluation of the HFX in a highly controllable manner. We show that our solutions can take great advantage of the latest trends in HPC platforms, such as extreme threading, short vector instructions and highly dimensional interconnection networks. Indeed, all these trends are evident in the IBM Blue Gene/Q supercomputer. We demonstrate an unprecedented scalability up to 6,291,456 threads (96 BG/Q racks) with a near perfect parallel efficiency.