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Publication# Efficient evaluation of accuracy of molecular quantum dynamics using dephasing representation

Résumé

Ab initio methods for the electronic structure of molecules have reached a satisfactory accuracy for calculations of static properties but remain too expensive for quantum dynamics calculations. We propose an efficient semiclassical method for evaluating the accuracy of a lower level quantum dynamics, as compared to a higher level quantum dynamics, without having to perform any quantum dynamics. The method is based on the dephasing representation of quantum fidelity and its feasibility is demonstrated on the photodissociation dynamics of CO2. Our accuracy test can be easily implemented in existing molecular dynamics codes, thus offering wide applicability.

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Concepts associés (8)

Dynamique moléculaire

La dynamique moléculaire est une technique de simulation numérique permettant de modéliser l'évolution d'un système de particules au cours du temps. Elle est particulièrement utilisée en sciences de

Electronic structure

In physics, electronic structure is the state of motion of electrons in an electrostatic field created by stationary nuclei. The term encompasses both the wave functions of the electrons and the ene

Méthode ab initio de chimie quantique

Les méthodes ab initio de chimie quantique sont des méthodes de chimie numérique basées sur la chimie quantique. La méthode ab initio la plus simple de calcul de structure électronique est le schéma H

Publications associées (9)

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Quantum chemical methods are important tools for the predictions of electronic structure and energetics of molecules providing the interpretation of spectroscopic experiments and reaction mechanisms. In this thesis, density functional theory (DFT) and wavefunction-based methods are used in order to evaluate their ability in predicting experimental data with a particular attention to photoprocesses occurring in both gas and condensed phase systems. The cases studied in this work are inspired by problems both from biology and material science. In the first study, the photoexcitation properties of the molecule 7-hydroxyquinoline·(NH3)3, a prototypical molecular wire, are investigated. A concerted mechanism according to which all protons are transferred simultaneously in a fast process (∼ 100 fs) that amounts to the net transport of one proton from the oxygen to the nitrogen of 7-hydroxyquinoline is observed. In addition, the proton transfer pathway involves all three ammonia molecules and not only two as previously proposed. The presence of potential energy surface crossings with a dark-state is responsible for the low experimentally observed quantum-yield. To better understand the complex photophysics of the amino acid tryptophan, which is widely used as a probe of protein structure, we performed DFT and TDDFT calculations of gas phase tryptophan solvated with a controlled number of water molecules. The addition of two water molecules sufficiently lengthens the excited state lifetime enabling vibrationally resolved spectra. Quantum chemical calculations at the RI-CC2/aug-cc-pVDZ level, together with TDDFT/pw based first-principles MD simulations of the excited state dynamics, clearly demonstrate how interactions with water destabilize the photodissociative states and increase the excited state lifetime. Due to the availability of high-resolution experimental data, this system is ideally suited as benchmark model for the evaluation of the performance of different quantum chemical methods. An extensive low-energy isomer search was carried out for [TrpH·(H2O)n=0,1,2]+ using a hierarchy of theoretical methods ranging from classical force fields to a variety of DFT methods (BLYP, B3LYP, M05, M05-2X, M06, M06-2X and M06-HF with different basis sets) up to the CBS-C level. For the low-energy structures, the harmonic vibrational frequencies are calculated and compared with high resolution experimental IR spectra. It turns out that in all three cases, CBS-C is able to predict the lowest energy isomers that are in agreement with the experimentally observed vibrational spectra. In most cases, M06 provides energetics in close agreement with the CBS-C results. On the other hand, M05-2X is the only functional that yields highly-reliable predictions of the vibrational spectra. A natural extension of the tryptophan model to condensed phase was performed by an investigation of the [Trp-Lys]+ motif studied in the protein Human Serum Albumin via QM/MM simulations. Like in the case of gas phase [TrpH]+, solvation effects lead to an increase of the σ*N-H orbital energies. As a result, the first photoaccessible state of sW K+ is primarily a photostable π* orbital, while in dW K+, photoexcitation leads to a dissociative pathway. The last application of this work concerns the optical properties of a novel dye for the sensitization of titanium dioxyde nanoparticles in Grätzel solar cells. The presence of a new absorption band in the visible region opens the way for a rational design of new dyes with improved properties.

Jiri Vanicek, Tomas Zimmermann

We propose an approximate method for evaluating the importance of non-Born–Oppenheimer effects on the quantum dynamics of nuclei. The method uses a generalization of the dephasing representation (DR) of quantum fidelity to several diabatic potential energy surfaces and its computational cost is the cost of dynamics of a classical phase space distribution. It can be implemented easily into any molecular dynamics program and also can utilize on-the-fly ab initio electronic structure information. We test the methodology on three model problems introduced by Tully and on the photodissociation of NaI. The results show that for dynamics close to the diabatic limit, the decay of fidelity due to nondiabatic effects is described accurately by the DR. In this regime, unlike the mixed quantum-classical methods such as surface hopping or Ehrenfest dynamics, the DR can capture more subtle quantum effects than the population transfer between potential energy surfaces. Hence we propose using the DR to estimate the dynamical importance of diabatic, spin-orbit, or other couplings between potential energy surfaces. The acquired information can help reduce the complexity of a studied system without affecting the accuracy of the quantum simulation.

Julien Ruppen, Jiri Vanicek, Tomas Zimmermann

Ab initio electronic structure methods have reached a satisfactory accuracy for the calculation of static properties, but remain too expensive for quantum dynamical calculations. Recently, an efficient semiclassical method was proposed to evaluate the accuracy of quantum dynamics on an approximate potential without having to perform the expensive quantum dynamics on the accurate potential. Here, this method is applied for the first time to evaluate the accuracy of quantum dynamics on an approximate analytical or interpolated potential in comparison to the quantum dynamics on an accurate potential obtained by an ab initio electronic structure method. Specifically, the vibrational dynamics of H2 on a Morse potential is compared with that on the full CI potential, and the photodissociation dynamics of CO2 on a LEPS potential with that on the excited 1^Pi surface computed at the EOM-CCSD/aug-cc-pVDZ level of theory. Finally, the effect of discretization of a potential energy surface on the quantum dynamics is evaluated.