Far Off Equilibrium Dynamics in Clusters and Molecules (original) (raw)
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Physics Reports, 2015
There are various ways to analyze the dynamical response of clusters and molecules to electromagnetic perturbations. Particularly rich information can be obtained from measuring the properties of electrons emitted in the course of the excitation dynamics. Such an analysis of electron signals covers observables such as total ionization, Photo-Electron Spectra (PES), Photoelectron Angular Distributions (PAD), and ideally combined PES/PAD. It has a long history in molecular physics and was increasingly used in cluster physics as well. Recent progress in the design of new light sources (high intensity, high frequency, ultra short pulses) opens new possibilities for measurements and thus has renewed the interest on these observables, especially for the analysis of various dynamical scenarios, well beyond a simple access to electronic density of states. This, in turn, has motivated many theoretical investigations of the dynamics of electronic emission for molecules and clusters up to such a complex and interesting system as C60. A theoretical tool of choice is here Time-Dependent Density Functional Theory (TDDFT) propagated in real time and on a spatial grid, and augmented by a Self-Interaction Correction (SIC). This provides a pertinent, robust, and efficient description of electronic emission including the detailed pattern of PES and PAD. A direct comparison between experiments and well founded elaborate microscopic theories is thus readily possible, at variance with more demanding observables such as for example fragmentation or dissociation cross sections.
Molecular dynamics in electronically excited states using time-dependent density functional theory
Molecular Physics, 2005
We describe two different implementations of time-dependent density functional theory (TDDFT) for use in excited state molecular dynamics simulations. One is based on the linear response formulation (LR-TDDFT), whereas the other uses a time propagation scheme for the electronic wave functions (P-TDDFT). Photo-induced cis-trans isomerization of C¼C, C¼N and N¼N double bonds is investigated in three model compounds, namely the 2,4-pentadiene-1-iminium cation (PSB), formaldimine and diimide. For formaldimine and diimide, the results obtained with both schemes are in agreement with experimental data and previously reported theoretical results. Molecular dynamics simulations yield new insights into the relaxation pathways in the excited state. For PSB, which is a model system for the retinal protonated Schiff base involved in the visual process, the forces computed from the LR-TDDFT S 1 surface lead to an increased bond length alternation and, consequently, to single bond rotation. On the contrary, P-TDDFT dynamics lead to a decreased bond length alternation, in agreement with CASPT2 and restricted open-shell Kohn-Sham (ROKS) calculations.
Excited states dynamics in time-dependent density functional theory
The European Physical Journal D - Atomic, Molecular and Optical Physics, 2004
We present a theoretical description of femtosecond laser induced dynamics of the hydrogen molecule and of singly ionised sodium dimers, based on a real-space, real-time, implementation of time-dependent density functional theory (TDDFT). High harmonic generation, Coulomb explosion and laser induced photo-dissociation are observed. The scheme also describes non-adiabatic effects, such as the appearance of even harmonics for homopolar but isotopically asymmetric dimers, even if the ions were treated classically. This TDDFT-based method is reliable, scalable, and extensible to other phenomena such as photoisomerization, molecular transport and chemical reactivity.
Physical Review Letters, 2008
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations. 71.15.Pd, 31.15.Ew Ab initio molecular dynamics (AIMD) on the ground state Born-Oppenheimer (gsBOMD) potential energy surface for the nuclei has become a standard tool for simulating the conformational behaviour of molecules, bioand nano-structures and condensed matter systems from first principles [1]. However, gsBOMD (in the DFT [2] picture) requires that the Kohn-Sham (KS) energy functional be minimized for each value of the nuclei positions. As this minimization can be very demanding, Car and Parrinello (CP) proposed an elegant and efficient "on the fly" scheme in which the KS orbitals are propagated with a fictitious dynamics that mimics gsBOMD. The CP method has had a tremendous impact in many scientific areas . Nevertheless, the numerical cost of AIMD hinders the application of the method to large scale simulations, such as those of interest in biochemistry or material science. Recently, new methods that allow larger systems and longer simulation times to be studied have been reported [6], but the cost associated with the wave function orthogonalization is still a potential bottleneck for both gsBOMD and CP.
The Journal of Chemical Physics, 2014
This article presents a time dependent density functional theory (TDDFT) implementation to propagate the Kohn-Sham equations in real time, including the effects of a molecular environment through a Quantum-Mechanics Molecular-Mechanics (QM-MM) hamiltonian. The code delivers an all-electron description employing Gaussian basis functions, and incorporates the Amber force-field in the QM-MM treatment. The most expensive parts of the computation, comprising the commutators between the hamiltonian and the density matrix-required to propagate the electron dynamics-, and the evaluation of the exchange-correlation energy, were migrated to the CUDA platform to run on graphics processing units, which remarkably accelerates the performance of the code. The method was validated by reproducing linear-response TDDFT results for the absorption spectra of several molecular species. Two different schemes were tested to propagate the quantum dynamics: (i) a leapfrog Verlet algorithm, and (ii) the Magnus expansion to first-order. These two approaches were confronted, to find that the Magnus scheme is more efficient by a factor of six in small molecules. Interestingly, the presence of iron was found to seriously limitate the length of the integration time step, due to the high frequencies associated with the core-electrons. This highlights the importance of pseudopotentials to alleviate the cost of the propagation of the inner states when heavy nuclei are present. Finally, the methodology was applied to investigate the shifts induced by the chemical environment on the most intense UV absorption bands of two model systems of general relevance: the formamide molecule in water solution, and the carboxy-heme group in Flavohemoglobin. In both cases, shifts of several nanometers are observed, consistently with the available experimental data.
Time-dependent density-functional theory method in the electron nuclear dynamics framework
Chemical Physics Letters, 2010
A time-dependent density-functional theory (DFT) dynamics method in the electron nuclear dynamics (END) framework is presented. This time-dependent variational method treats simultaneously the nuclei and electrons of a system without utilizing predetermined potential energy surfaces. Like the simplestlevel END, this method adopts a classical-mechanics description for the nuclei and a Thouless singledeterminantal representation for the electrons. However, the electronic description is now expressed in a Kohn-Sham DFT form that provides electron correlation effects absent in the simplest-level END. Current implementation of this method employs the adiabatic approximation in the exchange-correlation action and potential. Simulations of molecular vibrations and proton-molecule reactions attest to the accuracy of the present method.
The Journal of Chemical Physics, 2001
An extensive benchmarking of exchange-correlation functionals, pseudopotentials, and basis sets on real X-ray resolved nanoclusters has been carried out and reported here for the first time. The systems investigated and used for the tests are two undecagold and one Au + 24 -based nanoparticles stabilized by thiol and phosphine ligands. Time-dependent density-functional calculations have been performed for comparing results with experimental data on optical gaps. It has been observed that GGA functionals employing PBE-like correlation (viz. PBE itself, BPBE, BP86, and BPW91) coupled with an improved version of the LANL2DZ pseudopotential and basis set provide fairly accurate results for both structure and optical gaps of gold nanoparticles, at a reasonable computational cost. Good geometries have been also obtained using some global hybrid (e.g. PBE0, B3P86, B3PW91) and range separated hybrid (e.g. HSE06, LC-BLYP) functionals, even though they yield optical gaps that constantly overestimate the experimental findings. To probe the effect of the stabilizing organic ligands on the structural and electronic properties of the metal core, we have simulated the full metalorganic nanoparticles (whose diameter exceed the 2 nm threshold) with an ONIOM QM/QM' approach and at the density-functional level of theory. This work represents a first step toward the simulations of structural and opto-electronic properties of larger metal-organic particles suitable for a wide range of nanotechnological applications.
2011
Ziel dieser Arbeit war die Entwicklung einer allgemein anwendbaren Methode für die Simulation von ultraschnellen Prozessen und experimentellen Observablen. Hierfür wurden die Berechnung der elektronischen Struktur mit der zeitabhängigen Dichtefunktionaltheorie (TDDFT) und das Tully-Surface-Hopping-Verfahren für die nichtadiabatische Kerndynamik auf der Basis klassischer Trajektorien miteinander kombiniert. Insbesondere wurde eine Beschreibung der nichtadiabatischen Kopplungen für TDDFT entwickelt. Diese Methode wurde für die Simulation noch komplexerer Systeme durch die Tight-Binding-Näherung für TDDFT erweitert. Da die zeitaufgelöste Photoelektronenspektroskopie (TRPES) ein exzellentes experimentelles Verfahren für die Echtzeitbeobachtung von ultraschnellen Prozessen darstellt, wurde eine TDDFT-basierte Methode für die Simulation von TRPES entwickelt. Der Methode liegt die Idee zu Grunde, das System aus Kation und Photoelektron näherungsweise durch angeregte Zustände des neutralen Moleküls oberhalb der Ionisierungsgrenze zu beschreiben. Um diese Zustände mit TDDFT berechnen zu können wurde eine Beschreibung der Übergangsdipolmomente zwischen angeregten TDDFT-Zuständen entwickelt. Des Weiteren wurden Simulationen im Rahmen des Stieltjes-Imaging-Verfahrens, das eine Möglichkeit der Rekonstruktion des Photoelektronenspektrums aus den spektralen Momenten bietet, durchgeführt. Diese spektralen Momente wurden aus den diskreten TDDFT-Zuständen berechnet. Die breite Anwendbarkeit der entwickelten theoretischen Methoden für die Simulation von komplexen Systemen wurde an der Photoisomerisierung in Benzylidenanilin sowie der ultraschnellen Photodynamik in Furan, Pyrazin und mikrosolvatisiertem Adenin illustriert. Die dargestellten Beispiele demonstrieren, dass die nichtadiabatische Dynamik im Rahmen von TDDFT bzw. TDDFTB sehr gut für die Untersuchung und Interpretation der ultraschnellen photoinduzierten Prozesse in komplexen Molekülen geeignet ist.
Formal foundations of dressed time-dependent density-functional theory for many-electron excitations
2010
In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays however the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very much like what the local density approximation (LDA) is to conventional ground-state DFT. While some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this article will focus on many-body corrections to LR-TD-DFT as one way to building hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.
Time-dependent density functional theory employing optimized effective potentials
The Journal of Chemical Physics, 2002
Exchange-only ab initio ͑parameter-free͒ time-dependent density functional calculations for the vertical excitation energies of atoms and polyatomic molecules are performed by employing optimized effective potentials ͑OEP's͒ and their corresponding adiabatic exchange kernels for the first time. Accurate OEP's are obtained by a novel linear-combination-of-atomic-orbital ͑LCAO͒ algorithm ͓R. Colle and R. K. Nesbet, J. Phys. B 34, 2475 ͑2001͔͒ in which a potential is represented as a sum of a seed potential having the correct Ϫ1/r asymptotic behavior and a small and rapidly decaying correction, the latter being approximated accurately by a linear combination of Gaussian functions. The time-dependent OEP ͑TDOEP͒ methods with and without the Tamm-Dancoff approximation are implemented by using a trial-vector algorithm, which allows us to avoid the storage or manipulation of transformed two-electron integrals or the diagonalization of large matrices. No approximation is made to TDOEP, besides the adiabatic approximation to the exchange kernel, the LCAO expansion of the orbitals and potentials, and occasionally the Tamm-Dancoff approximation. The vertical excitation energies of the beryllium atom and the nitrogen and water molecules calculated by TDOEP are compared with those obtained from time-dependent density functional theory ͑TDDFT͒ employing conventional local or gradient-corrected functionals, configuration interaction singles ͑CIS͒, time-dependent Hartree-Fock ͑TDHF͒ theory, similarity-transformed equation-of-motion coupled-cluster with single and double substitutions, and experiments. TDOEP, which neglects electron correlation while treating the exchange contribution rigorously within the Kohn-Sham DFT framework, performs equally well as, or even appreciably better than, CIS or TDHF. The slightly better performance of TDOEP might be attributed to the local nature of the exchange potentials that allows the bare orbital energy differences to approximate excitation energies well. Nevertheless, TDDFT employing local or gradient-corrected functionals outperforms TDOEP for low-lying valence excited states, implying that the former somehow accounts for electron correlation effectively, whereas for high-lying and Rydberg excited states, the latter performs better than the former. By combining the desirable features of OEP and local or gradient-corrected exchange-correlation potentials, we arrive at a simple asymptotic correction scheme to the latter. TDDFT with the asymptotic correction yields uniformly accurate excitation energies for both valence and Rydberg excited states.