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Excitation-energy transfer (EET) and relaxation in an optically excited building block of poly(phenylene ethynylene) (PPE) dendrimers are simulated using wavepackets with the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and reduced-density matrices with the hierachical equations of motion (HEOM) approach. The dynamics of the ultrafast electronic funneling between the first two excited electronic states in the asymmetrically meta-substituted PPE oligomer with two rings on one branch and three rings on the other side, with a shared ring in between, is treated with 93-dimensional ab initio vibronic-coupling Hamiltonian (VCH) models, either linear or with bilinear and quadratic terms. The linear VCH model is also used to model an open quantum system. The linear-response absorption and emission spectra are simulated with both the ML-MCTDH and HEOM methods. The latter is further used to explore the nonlinear response regime and the expected EET fingerprint in the time-resolved transient absorption (TA) spectra and excited stimulated emission (ESE) with delta-like impulsive laser pulses., Comment: 20 pages of manuscript, 15 pages of supplementary materials

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like {\pi}-conjugated macromolecules) involve a directional cascade of local excitation-energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally-excited (LE) electronic states via conical intersections. The smallest PPE building block able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From time-dependent density-functional theory (TD-DFT) electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1+2)-state-8-dimensional vibronic-coupling Hamiltonian (VCH) model for running multiconfiguration time-dependent Hartree (MCTDH) wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra, as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25 fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity., Comment: 19 pages of manuscript, 20 pages of supplementary information

This work presents an alternative, general, and in-principle exact extension of electronic Kohn-Sham density functional theory (KS-DFT) to the fully quantum-mechanical molecular problem. Unlike in existing multi-component or exact-factorization-based DFTs of electrons and nuclei, both nuclear and electronic densities are mapped onto a fictitious electronically non-interacting molecule (referred to as KS molecule), where the electrons still interact with the nuclei. Moreover, in the present molecular KS-DFT, no assumption is made about the mathematical form (exactly factorized or not) of the molecular wavefunction. By expanding the KS molecular wavefunction \`a la Born-Huang, we obtain a self-consistent set of "KS beyond Born-Oppenheimer" electronic equations coupled to nuclear equations that describe nuclei interacting among themselves and with non-interacting electrons. An exact adiabatic connection formula is derived for the Hartree-exchange-correlation energy of the electrons within the molecule and, on that basis, a practical adiabatic density-functional approximation is proposed and discussed., Comment: 16 pages

In this work, we introduce an original self-consistent scheme based on the one-body reduced density matrix ($\gamma$) formalism. A significant feature of this methodology is the utilization of an optimal unitary transformation of the Hamiltonian, determined through a self-consistently determined, unitary reflection $\mathbf{R}[\gamma]$. This enables the extraction of all reduced properties of the system from a smaller, accurately solved embedding cluster, and to systematically reconstruct the reduced density matrix of the system. This process ensures that both extended and embedded systems satisfy the local virial-like relation, providing quantitative insight into the correspondence between the fragment in the extended system and its embedded analogue. The performance and convergence of the method, as well as the N-representability of the resulting correlated density matrix, are evaluated and discussed within the context of the one-dimensional Hubbard model, which provides exact results for a comprehensive comparison.

1,3-bis(phenylethynyl)benzene is the primary chromophore of light-harvesting polyphenylene ethynylene (PPE) dendrimers. It is experimentally known to share the same absorption spectrum as its pair of diphenylacetylene (aka. tolane) meta-substituted branches, yet exhibits an unusual Stokes shift of about 2000 cm$^{-1}$ with respect to its band origin (corresponding to the loss of one vibrational quantum within the antisymmetric acetylenic stretching) in its emission spectrum. We suggest in the present work the unusual but plausible involvement of molecular symmetry selection rules in a situation where the Born-Oppenheimer approximation is far to be valid. Our hypothesis is comforted with quantum dynamics (MCTDH) simulations of absorption and emission UV-visible spectra based on quantum chemistry (TD-DFT) data and a diabatic vibronic coupling Hamiltonian model., Comment: 15 pages of manuscript, 15 pages of supplementary information

Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were formally described in our previous work [I. Burghardt, R. Carles, C. Fermanian Kammerer, B. Lasorne, C. Lasser, J. Phys. A. 54, 414002 (2021)]. Specifically, we consider a representative two-dimensional tunneling system where a double well and a harmonic coordinate are cubically coupled. The timedependent Hartree approximation is compared with a fully correlated solution, for different parameter regimes. The impact of the coupling and the resulting correlations are quantitatively assessed in terms of a time-dependent reaction probability along the tunneling coordinate. We show that the numerical error is correctly predicted on moderate time scales by a theoretically derived error estimate.

In this work, we introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Ref. [S. Yalouz et al. ,Quantum Sci. Technol. 6, 024004 (2021).]). Motivated by the limitations of current quantum computers, the first extension consists in an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and non-adiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH$_2$NH (a minimal Schiff base model relevant for the study of photoisomerization in larger bio-molecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule., Comment: 22 pages, 7 figures

We consider composite quantum-dynamical systems that can be partitioned into weakly interacting subsystems, similar to system-bath type situations. Using a factorized wave function ansatz, we mathematically characterize dynamical scale separation.Specifically, we investigate a coupling r{\'e}gime that is partially flat, i.e., slowly varying with respect to one set of variables, for example, those of the bath. Further, we study the situation where one of the sets of variables is semiclassically scaled and derive a quantum-classical formulation. In both situations, we propose two schemes of dimension reduction: one based on Taylor expansion (collocation) and the other one based on partial averaging (mean-field). We analyze the error for the wave function and for the action of observables, obtaining comparable estimates for both approaches. The present study is the first step towards a general analysis of scale separation in the context of tensorized wavefunction representations., Comment: Title changed, Section 3.3 reorganized, new Section 6 (numerical example)

Nonadiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natural intersections. In this work we show that the standard low-energy vibrational spectrum of the electronic ground state can change dramatically by inducing nonadiabaticity via a light-induced conical intersection. This generic effect is demonstrated for an explicit example by full-dimensional high-level quantum calculations using a pump-probe scheme with a moderate-intensity pump laser and a weak probe laser.

In this paper we discuss the reliability of two computational methods (numerical integration on Cartesian grids, and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These descriptors are integrals of charge density functions built from the detachment and attachment density matrices projected in the Euclidean space using a finite basis of orbitals. While the numerical integration on Cartesian grids is easily considered to be converged for medium-sized density grids, the population analysis approximation to the numerical integration values is diagnosed using eight diagnostic tests performed on fifty-nine molecules with a combination of fifteen Gaussian basis sets and six exchange-correlation functionals.

Numerical simulations are presented to validate the possible use of cutting-edge attosecond time- resolved photoelectron spectroscopy to observe in real time the creation of an electronic wavepacket and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds.

A coherent superposition of two electronic states of ozone (ground and Hartley B) is prepared with a UV pump pulse. Using the multiconfiguration time-dependent Hartree approach, we calculate the subsequent time evolution of the two corresponding nuclear wave packets and the coherence between them. The resulting wave packet shows an oscillation between the two chemical bonds. Even more interesting, the coherence between the two electronics states reappears after the laser pulse is switched off, which could be observed experimentally with an attosecond probe pulse.