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

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.

Non-adiabatic Dynamics Using Time-Dependent Density Functional Theory: assessing the Coupling Strengths

Ursula Röthlisberger, Enrico Marko Tapavicza, Ivano Tavernelli

Light-driven reactions constitute an important class of processes in physics, chemistry, and biology. The development of accurate and efficient computational tools for the study of excited states dynamics has thus become of primary importance. Recently, we have developed a non-adiabatic ab initio molecular dynamics (AIMD) method, which combines Tully's surface hopping with TDDFT. Here, we investigate some fundamental aspects of this AIMD scheme that deal with the accuracy of TDDFT potential energy surfaces in regions of strong coupling and with the associated intensity of the non-adiabatic couplings (NACs). Of particular interest is the coupling between the ground and the first excited singlet state, which constitute a potential pitfall for all non-adiabatic AND based on TDDFT. To this end, we have investigated the excited state dynamics of protonated formaldimine (CH2NH2+) with particular emphasis on the analysis of the NAC strengths in regions of the configurational space close to surface hopping points and conical intersections. A good agreement of the structural and dynamical properties is found with respect to state averaged multiconfiguration self consistent field results. (C) 2009 Elsevier B.V. All rights reserved.

2009

A Classical and Quantum Trajectory Description of Nonadiabatic Dynamics within Time-Dependent Density Functional Theory

Basile Curchod

Characterizing and predicting the nuclear dynamics of electronically excited molecules is of paramount importance to the understanding of photochemical and photophysical processes in molecules and to the development of new technologies in domains like solar energy conversion, efficient illumination devices, and medicine. However, the theoretical description of such phenomena remains a challenge for theoretical chemists. The most notable difficulty comes from the breakdown of the widely used Born-Oppenheimer approximation, which considers the time evolution of the nuclei fully decoupled from the one of the electrons. Moving beyond this approximation requires the inclusion of nonadiabatic effects, which induces an entangled electron-nuclear dynamics. Additionally, the convenient approximation that the motion of the nuclear degrees of freedom can be described with classical mechanics is likely to fail in the case of nonadiabatic events. While several theoretical techniques have been proposed to treat both the electronic structure and the nonadiabatic dynamics problems, they all rely on a compromise between accuracy and efficiency. The principal goal of this thesis is to improve the description of molecular nonadiabatic phenomena using classical and quantum trajectories, combined with linear-response time-dependent density functional theory (LR-TDDFT) for the calculation of the electronic structure properties. In the first part of this work, we review several methods used to solve exactly or in an approximate way the nuclear time-dependent Schrödinger equation with quantum or classical trajectories. We then move on to show how the molecular time-dependent Schrödinger equation can be reformulated exactly in terms of quantum trajectories evolving in coupled adiabatic electronic states. This nonadiabatic Bohmian dynamics (NABDY) scheme allows for the description of all nuclear quantum effects like decoherence and tunneling, and is compatible with a nuclear wavepacket dynamics in which the electronic structure information is computed on-the-fly. Furthermore, we discuss how NABDY can be related, through several approximations, to the trajectory surface hopping (TSH) method, which is one of the most commonly applied on-the-fly trajectory-based techniques to describe the dynamics of molecular systems beyond the Born-Oppenheimer approximation in (the unconstrained) configuration space of molecules. The TSH method describes the nuclear wavepacket dynamics with a swarm of uncorrelated classical trajectories, consequently banishing all nuclear quantum effects. Understanding the underlying limitations of TSH is of foremost importance for the improvement of the theory. In this thesis, several one dimensional model systems are used to assess the accuracy of TSH through a comparison with the correlated NABDY dynamics. In the second part, we focus on the electronic structure problem and discuss how LR-TDDFT can be used in the implementation of an efficient on-the-fly nonadiabatic molecular dynamics scheme. Within this theory, all the electronic information needed, namely excitation energies, excited state nuclear forces, nonadiabatic couplings, and other electronic matrix elements, have to be represented as a functional of the electronic density. We show how the concept of auxiliary many-electron wavefunction can be used to compute the matrix elements of any one-body operators. In the third and last part, we discuss two extensions of the TSH method based on LR-TDDFT, aimed at describing the effects of the environment on a molecular system in the most possible realistic way. First, the effects of an explicit solvent on a photoactive solute is described within a QM/MM formalism. The resulting TSH/LR-TDDFT/MM scheme is applied to the nonradiative relaxation of the inorganic compound ruthenium (II) trisbipyridine in water. This application further highlights the need for the inclusion of relativistic effects in the TSH algorithm such as spin-orbit coupling to describe intersystem crossing processes. Second, the TSH equations are coupled with an external time-dependent electric field, such that photoexcitation processes can be naturally described within this mixed quantum/classical method. The electric field can be either parametrized or shaped to selectively maximize the population of a given target electronic state. TSH dynamics coupled to an electric field is first applied to the study of the photodissociation dynamics of a diatomic molecule (lithium fluoride) and then used for the investigation of the photoinduced proton transfer reaction in an organic compound (4-hydroxyacridine). This thesis presents several possibilities to describe the nonadiabatic dynamics of molecules. In addition, it also highlights some current limitations of both electronic structure and nonadiabatic dynamics methods, proposing new potential solutions to these problems.

EPFL2013

Capturing Non-local Effects in Kohn-Sham Density Functional Theory

Andrey Laktionov

Density Functional Theory (DFT) and its time-dependent extension (TDDFT) have become two of the most popular approaches for computer simulations of the electronic structure and response properties of quantum systems. A reasonable compromise between accuracy and computational cost allows to apply DFT to a wide range of systems from small molecules to biological complexes. Despite the in principle exact nature of DFT and TDDFT, practical calculations require the use of approximate DFT exchange-correlation (XC) functionals and TDDFT kernels and the accuracy of the obtained results is determined by the accuracy of the chosen XC description. These approximations inevitably introduce some limitations in the use of DFT-based methods.The inability of the local spin density approximation, generalized gradient approximations (GGA) and even some hybrid functionals to properly describe charge transfer (CT) excitations and predict intermolecular interaction energies of weakly bound complexes are two major drawbacks of current XC descriptions. This thesis is therefore devoted to the improvement of XC functionals for the special cases of weak interactions and charge-transfer excitations. Many original strategies have been suggested to cure DFT calculations from these failures. In particular, the Dispersion-Corrected Atom-Centered Potentials (DCACP) approach provides an accurate description of dispersion forces within generalized gradient approximations for the exchange-correlation functional. The DCACP method has been extensively used for the last seven years and has shown an excellent performance for a large class of applications. However, one of the drawbacks of the current implementation of DCACP is that the correct R-6 asymptotics of dispersion interaction is not reproduced. A first goal of this thesis was to enable DCACP to recover the R-6 asymptotic limit. To this end, we have designed a new 2-channel version of DCACP and carried out test calculations on both small molecules and large macromolecular complexes. The obtained results demonstrate the excellent performance and transferability of the DCACP approach. Moreover, for large macromolecular complexes, in which the binding energy is dominated by dispersion, [pi]-stacking, or hydrogen bonding, 2-channels DCACP were found to be the best method overall for correcting the popular BLYP functional. Our study clearly shows that account of R-6 asymptotics is crucial for the description of large complexes and that 2-channels DCACP are fully able to capture these effects. On the contrary, an account of R-6 asymptotics is of little importance for small molecules since the remaining errors of the underlying GGA functional are dominating. With the aim of deepening our understanding of the DCACP concept and the reasons for its excellent performance, we explored the properties of the two DCACP parameters and were able to establish some systematic trends. It turned out that variational tuning of the DCACP can be done in an analytical manner that enables the easy generation of DCACP potentials for the full periodic table. Furthermore, since DCACP have little but crucial impact on the electronic density, dispersion energies can be obtained from non-self-consistent electron densities. These empirical findings suggest that the high transferability of DCACP is due to their atom-centered form and the intrinsically weak nature of dispersion interactions. [...]