Improving Performance and Accuracy of Hybrid-Functional Based Molecular Dynamics in Plane Waves

The simulation of condensed matter in first principles Molecular Dynamics (FPMD) heavily relies on Kohn-Sham Density Functional Theory (KS-DFT) calculations. The accuracy of such simulations is governed by the reliability of the underlying potential energy surface (PES) and the accessible time scale; both factors are crucially influenced by the choice of exchange-correlation (xc) functional. Hybrid xc functionals, which include a fraction of exact exchange, are among the most accurate xc approximations available. However, in particular in combination with the plane wave basis commonly used in FPMD, the computational overhead due to the evaluation of exchange integrals significantly limits the time scale of the simulation, thus hampering convergence of observables. This work aims at improving the availability of hybrid xc functionals in a plane wave basis while reducing their computational overhead. Part I provides an introduction to the field of FPMD. Starting from the quantum mechanical partition function, we show the simplifications behind the single-state Born-Oppenheimer approximation, followed by a discussion of the theoretical foundations of KS-DFT, an overview of practical approximations, and their implementation in a plane wave/pseudopotential formalism. In Part II, we outline the implementation and performance of two popular families of xc functionals. We first derive the plane wave expressions for the Coulomb-Attenuation Method (CAM) and compare its performance in a plane wave basis to common atom-centred basis sets. A new xc functional, CAM-O3LYP, is reported, which outperforms the commonly employed CAM-B3LYP in some notorious cases. We then present the implementation of the M05 to M11 families of Minnesota functionals in a plane wave basis. A detailed convergence analysis suggests that a fine enough integration mesh has to be provided in order to obtain accurate energy differences, and a comparison of reaction enthalpies obtained in plane waves and atom-centred bases reveals an unusual sensitivity of certain Minnesota functionals to the choice of basis. We provide a rationale for the observed differences by comparing electron densities between different functionals and basis sets demonstrating that plane waves make it possible to conveniently obtain values for basis set limits for functionals that can be difficult to converge in atom-centred bases. Part III introduces a coordinate-scaling scheme for the calculation of exact exchange integrals for isolated systems in a plane wave basis. By applying the scaling relations of the exact exchange functional to the Hartree-Fock term, we show that it is possible to effectively reduce the cost of the Fast Fourier Transforms (FFT) that constitute the bottleneck of the calculation while retaining good accuracy. We then present the practical implementation and parallelisation of the method in the CPMD code and show that speedups can reach values of up to one order of magnitude, thereby considerably improving the computational footprint of hybrid functionals. In Part IV, we offer a perspective on further work by discussing recent additions to the library of dispersion-corrected atom-centred potentials (DCACP) and by introducing a method for structural refinement based on electron density difference maps, density-difference driven molecular dynamics (d3MD). We conclude by providing a brief overview of the results obtained in this work and by discussing future perspectives.

Development of a non-adiabatic ab initio molecular dynamics method and its application to photodynamical processes

Enrico Marko Tapavicza

Photoprocesses are ubiquitous in nature, science, and engineering. The understanding as well as the optimization of photochemical and photophysical properties of molecular systems requires computational tools that are able to describe the dynamical evolution of the system in electronically excited states. Ab Initio Molecular Dynamics (AIMD) based on Density Functional Theory (DFT) has become an established tool for elucidating mechanisms of chemical reactions that occur in the electronic ground state. However, to describe photoprocesses by AIMD, an underlying electronic-structure method that is able to treat excited states is necessary. This complicates the description of these processes because in the past this implied the use of computationally expensive wavefunction-based methods, which in addition are not straightforward to use. Time-Dependent Density Functional Theory (TDDFT) provides an in principle exact description of electronically excited states, although in practice, approximations have to be introduced. Compared to wavefunction-based methods, TDDFT is computationally less demanding and is relatively straightforward and easy to use. Recently, TDDFT nuclear gradients have become available and allow to carry out AIMD in excited states. In this thesis a TDDFT-based AIMD method that is able to account for non-adiabatic effects is developed and implemented. The non-adiabatic couplings are computed by means of a Kohn-Sham orbital based reconstruction of the many-electron wavefunction for ground and excited states. The non-adiabatic scheme is based on the fewest switches trajectory surface hopping (SH) method introduced by Tully. The method is applied to describe decay processes, such as fragmentation or isomerization, that occur upon photoexcitation of the molecules protonated formaldimine and oxirane. In the case of protonated formaldimine, the results of the TDDFT-SH method are in good agreement with SH simulations based on the state-averaged complete active space (SA-CASSCF) method, both with respect to the observed reaction mechanisms and the excited state life times. In the case of oxirane, the TDDFT-SH simulations confirm the main experimental results and provide an additional refinement of the postulated reaction mechanism. The accuracy of TDDFT is investigated with respect to different issues that are especially important for the proper description of photoprocesses. These aspects include the accuracy of non-adiabatic coupling (NAC) vectors, the description of S1-S0 conical intersections, and the description of locally excited states in systems where charge transfer (CT) states are present, that are affected by the well-known CT failure of TDDFT. Concerning the NAC vectors, a qualitative agreement with SA-CASSCF is found, although magnitudes are underestimated by TDDFT/PBE. Regarding the description of conical intersections to the ground state, we find as expected that TDDFT in the adiabatic approximation (ALDA) is not able to predict an intersection that is strictly conical. However, we find that TDDFT is able to approximate a conical intersection that has a similar shape as the one predicted by SA-CASSCF. For an electron donor-bridge-acceptor molecule it is shown that the CT failure of TDDFT can also considerably affect properties of non-CT states. The use of TDDFT using conventional exchange-correlation functionals is thus not recommended for the description of such systems. Using the second-order approximate coupled cluster (CC2) method in conjunction with a high quality basis set, an accurate and balanced description of both locally excited and CT states can be made. The use of CC2 with large basis sets for AIMD simulations is however still computationally unaffordable for larger systems. TDDFT is still in its infancy and several attempts to cure some of its defiencies have already been made. These attempts mainly concern improvements of the approximations of the exchange-correlation functionals and associated TDDFT kernels. The TDDFT-SH method that has been developed in this thesis can in principle be applied in combination with any approximation for the exchange correlation functional, provided that nuclear gradients for this approximation are available and the computational cost remains acceptable. In this way, the method developed here is able to directly profit from the ongoing improvements in the active research field of exchange-correlation functionals and kernels.

EPFL2008

Structural and electronic properties of an abrupt 4H-SiC(0001)/SiO2 interface model: Classical molecular dynamics simulations and density functional calculations

Peter Broqvist, Fabien Devynck, Alfredo Pasquarello

Using a density functional approach, we study structural and electronic properties of the 4H(0001)-SiC/SiO2 interface. Through the sequential use of classical and ab initio simulation methods, we generate an abrupt model structure which describes the transition between crystalline SiC and amorphous SiO2 without showing any coordination defect. The first step in our generation procedure consists in identifying suitable interfacial bonding patterns which account for the bond density reduction across the interface. In the second step, the connection to amorphous SiO2 is achieved through classical molecular dynamics. The atomic positions are then relaxed within a generalized gradient approximation of density functional theory. The final model structure shows good structural parameters and an oxide density typical of amorphous SiO2. We investigate the electronic structure of the generated model interface through the local density of states obtained with hybrid density functionals. In our atomically abrupt interface model, the full oxide band gap is recovered at a distance of similar to 5 A from the interface. This extent is in good agreement with estimates derived from internal photoemission measurements and provides support for the abrupt nature of the interface. We obtained band offsets through two different procedures: by evaluating the local density of states and by aligning the band extrema through the local electrostatic potential. Band offsets calculated with various functionals are compared to experimental values. The best agreement is achieved for a hybrid functional in which a screened Coulomb potential is used in the Hartree-Fock exchange term. For this case, the calculated band offsets underestimate the experimental values by similar to 25%, but agree with experiment within a few percent when expressed with respect to the oxide band gap.

2007

Development of a non-adiabatic ab initio molecular dynamics method and its application to photodynamical processes

Enrico Marko Tapavicza

EPFL2008

Structural and electronic properties of an abrupt 4H-SiC(0001)/SiO2 interface model: Classical molecular dynamics simulations and density functional calculations

Peter Broqvist, Fabien Devynck, Alfredo Pasquarello

2007