Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor

Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.

Photodissociation of deuterated pyrrole-ammonia clusters: H-atom transfer or electron coupled proton transfer?

Several years ago the discovery of a conical intersection offered an explanation for the ultafast photodissociation of pyrrole. Subsequently, the photodissociation of pyrrole ammonia complexes PyH*(NH3)n with n ≥ 3 was studied in the gas phase as a model for a hydrogen-bond forming solvent. Two alternative mechanisms, electron coupled proton transfer (ECPT) and hydrogen atom transfer (HAT, also called the impulsive model, IM), have been proposed. The parent 1 : 1 complex was never studied, due to the short lifetime of the NH4 radical fragment. Here we report experiments on the deuterated species PyD*(ND3)n, including the 1 : 1 complex (n = 1). The velocity distribution of the ND4 radical is well approximated by a Maxwell-Boltzmann distribution of T ≈ 530 K, with a negative anisotropy parameter of β = -0.3. The impulsive model predicts a much narrower velocity distribution with larger negative anisotropy. The ECPT model predicts a long lived intermediate that should allow thermal equilibration of the vibrational energy but should also destroy the rotational memory of the initially excited state. The average kinetic energy agrees with the prediction of the impulsive model, whereas the wide range of kinetic energies is more in line with ECPT. Hence the mechanism seems to be more complex and requires further theoretical modelling.

Quantum simulation of conical intersections

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

Can classical mechanics sense conical intersection?

Conical intersection (CI) leads to fast electronic energy transfer. However, Hamm and Stock [Phys. Rev. Lett. 109, 173201 (2012)] showed the existence of a vibrational CI and its role in vibrational energy relaxation. In this paper, we further investigate the vibrational energy relaxation using an isolated model Hamiltonian system of four vibrational modes with two distinctively different timescales (two fast modes and two slow modes). We show that the excitation of the slow modes plays a crucial role in the energy relaxation mechanism. We also analyze the system from a mixed quantum-classical (surface hopping method) and a completely classical point of view. Notably, surface hopping and even classical simulations also capture fast energy relaxation, which is a signature of CI's existence.

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Coherent x-ray spontaneous emission spectroscopy of conical intersections

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born-Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection.

Highly efficient implementation of analytic nonadiabatic derivative couplings within the pseudospectral method

A pseudospectral implementation of nonadiabatic derivative couplings in the Tamm-Dancoff approximation is reported, and the accuracy and efficiency of the pseudospectral nonadiabatic derivative couplings are studied. Our results demonstrate that the pseudospectral method provides mean absolute errors of 0.2%-1.9%, while providing a significant speedup. Benchmark calculations on fullerenes (Cn, n up to 100) using B3LYP achieved 10- to 15-fold, 8- to 17-fold, and 43- to 75-fold speedups for 6-31G**, 6-31++G**, and cc-pVTZ basis sets, respectively, when compared to the conventional spectral method.

On the multiphoton ionisation photoelectron spectra of phenol

The phenol molecule is a prototype for non-adiabatic dynamics and the excited-state photochemistry of biomolecules. In this article, we report a joint theoretical and experimental investigation on the resonance enhanced multiphoton ionisation photoelectron (REMPI) spectra of the two lowest ionisation bands of phenol. The focus is on the theoretical interpretation of the measured spectra using quantum dynamics simulations. These were performed by numerically solving the time-dependent Schrödinger equation using the multi-layer variant of the multiconfiguration time-dependent Hartree algorithm together with a vibronic coupling Hamiltonian model. The ionising laser pulse is modelled explicitly within the ionisation continuum model to simulate experimental femtosecond 1+1 REMPI photoelectron spectra. These measured spectra are sensitive to very short lived electronically excited states, providing a rigorous benchmark for our theoretical methods. The match between experiment and theory allows for an interpretation of the features of the spectra at different wavelengths and shows that there are features due to both 'direct' and 'indirect' ionisation, resulting from non-resonant and resonant excitation by the pump pulse.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Spin-Vibronic Dynamics in Open-Shell Systems beyond the Spin Hamiltonian Formalism

Vibronic coupling has a dramatic influence over a large number of molecular processes, ranging from photochemistry to spin relaxation and electronic transport. The simulation of vibronic coupling with multireference wave function methods has been largely applied to organic compounds, and only early efforts are available for open-shell systems such as transition metal and lanthanide complexes. In this work, we derive a numerical strategy to differentiate the molecular electronic Hamiltonian in the context of multireference ab initio methods and inclusive of spin-orbit coupling effects. We then provide a formulation of open quantum system dynamics able to predict the time evolution of the electron density matrix under the influence of a Markovian phonon bath up to fourth-order perturbation theory. We apply our method to Co(II) and Dy(III) molecular complexes exhibiting long spin relaxation times and successfully validate our strategy against the use of an effective spin Hamiltonian. Our study sheds light on the nature of vibronic coupling, the importance of electronic excited states in spin relaxation, and the need for high-level computational chemistry to quantify it.

Detailed balance in mixed quantum-classical mapping approaches

The violation of detailed balance poses a serious problem for the majority of current quasiclassical methods for simulating nonadiabatic dynamics. In order to analyze the severity of the problem, we predict the long-time limits of the electronic populations according to various quasiclassical mapping approaches by applying arguments from classical ergodic theory. Our analysis confirms that regions of the mapping space that correspond to negative populations, which most mapping approaches introduce in order to go beyond the Ehrenfest approximation, pose the most serious issue for reproducing the correct thermalization behavior. This is because inverted potentials, which arise from negative electronic populations entering the nuclear force, can result in trajectories unphysically accelerating off to infinity. The recently developed mapping approach to surface hopping (MASH) provides a simple way of avoiding inverted potentials while retaining an accurate description of the dynamics. We prove that MASH, unlike any other quasiclassical approach, is guaranteed to describe the exact thermalization behavior of all quantum-classical systems, confirming it as one of the most promising methods for simulating nonadiabatic dynamics in real condensed-phase systems.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

The carbonyl-lock mechanism underlying non-aromatic fluorescence in biological matter

Challenging the basis of our chemical intuition, recent experimental evidence reveals the presence of a new type of intrinsic fluorescence in biomolecules that exists even in the absence of aromatic or electronically conjugated chemical compounds. The origin of this phenomenon has remained elusive so far. In the present study, we identify a mechanism underlying this new type of fluorescence in different biological aggregates. By employing non-adiabatic ab initio molecular dynamics simulations combined with a data-driven approach, we characterize the typical ultrafast non-radiative relaxation pathways active in non-fluorescent peptides. We show that the key vibrational mode for the non-radiative decay towards the ground state is the carbonyl elongation. Non-aromatic fluorescence appears to emerge from blocking this mode with strong local interactions such as hydrogen bonds. While we cannot rule out the existence of alternative non-aromatic fluorescence mechanisms in other systems, we demonstrate that this carbonyl-lock mechanism for trapping the excited state leads to the fluorescence yield increase observed experimentally, and set the stage for design principles to realize novel non-invasive biocompatible probes with applications in bioimaging, sensing, and biophotonics.

Non-adiabatic coupling in the potential energy surfaces of SO2 molecule

To investigate the potential energy surfaces and the coupling between the adiabatic states of SO2 molecules, it is necessary to consider the non-adiabatic coupling terms (NACTs), where the Born-Oppenheimer approximation breaks down. In this work, we analyze the conical intersections between 1 1A1 and 1 1B2 states (the A' states in Cs symmetry) and 1 1A2 and 1 1B1 states (the A'' states in Cs symmetry) using NACTs and adiabatic-to-diabatic transformation (ADT) angles. Our results confirm reasonable interaction between 1 1A1 and 1 1B2 states and strong interaction between 1 1A2 and 1 1B1 states.

Deciphering Methylation Effects on S2(ππ*) Internal Conversion in the Simplest Linear α,β-Unsaturated Carbonyl

Chemical substituents can influence photodynamics by altering the location of critical points and the topography of the potential energy surfaces (electronic effect) and by selectively modifying the inertia of specific nuclear modes (inertial effects). Using nonadiabatic dynamics simulations, we investigate the impact of methylation on S₂(ππ*) internal conversion in acrolein, the simplest linear α,β-unsaturated carbonyl. Consistent with time constants reported in a previous time-resolved photoelectron spectroscopy study, S₂ → S₁ deactivation occurs on an ultrafast time scale (∼50 fs). However, our simulations do not corroborate the sequential decay model used to fit the experiment. Instead, upon reaching the S₁ state, the wavepacket bifurcates: a portion undergoes ballistic S₁ → S₀ deactivation (∼90 fs) mediated by fast bond-length alternation motion, while the remaining decays on the picosecond time scale. Our analysis reveals that methyl substitution, generally assumed to mainly exert inertial influence, is also manifested in important electronic effects due to its weak electron-donating ability. While methylation at the β C atom gives rise to effects principally of an inertial nature, such as retarding the twisting motion of the terminal -CHCH₃ group and increasing its coupling with pyramidalization, methylation at the α or carbonyl C atom modifies the potential energy surfaces in a way that also contributes to altering the late S₁-decay behavior. Specifically, our results suggest that the observed slowing of the picosecond component upon α-methylation is a consequence of a tighter surface and reduced amplitude along the central pyramidalization, effectively restricting the access to the S₁/S₀-intersection seam. Our work offers new insight into the S₂(ππ*) internal conversion mechanisms in acrolein and its methylated derivatives and highlights site-selective methylation as a tuning knob to manipulate photochemical reactions.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Intermolecular-Type Conical Intersections in Benzene Dimer

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

The principal component analysis of the ring deformation in the nonadiabatic surface hopping dynamics

The analysis of the leading active molecular motions in the on-the-fly trajectory surface hopping simulation provides the essential information to understand the geometric evolution in nonadiabatic dynamics. When the ring deformation is involved, the identification of the key active coordinates becomes challenging. A "hierarchical" protocol based on the dimensionality reduction and clustering approaches is proposed for the automatic analysis of the ring deformation in the nonadiabatic molecular dynamics. The representative system keto isocytosine is taken as the prototype to illustrate this protocol. The results indicate that the current hierarchical analysis protocol is a powerful way to clearly clarify both the major and minor active molecular motions of the ring distortion in nonadiabatic dynamics.

Nonadiabatic Excited State Dynamics of Organic Chromophores: Take-Home Messages

Nonadiabatic excited state dynamics are important in a variety of processes. Theoretical and experimental developments have allowed for a great progress in this area, while combining the two is often necessary and the best approach to obtain insight into the photophysical behavior of molecules. In this Feature Article we use examples of our recent work combining time-resolved photoelectron spectroscopy with theoretical nonadiabatic dynamics to highlight important lessons we learned. We compare the nonadiabatic excited state dynamics of three different organic molecules with the aim of elucidating connections between structure and dynamics. Calculations and measurements are compared for uracil, 1,3-cyclooctadiene, and 1,3-cyclohexadiene. The comparison highlights the role of rigidity in influencing the dynamics and the difficulty of capturing the dynamics accurately with calculations.

Accurate Non-Adiabatic Couplings from Optimally-Tuned Range-Separated Hybrid Functionals

Precise theoretical calculations of non-adiabatic couplings, which describe the interaction between two Born-Oppenheimer surfaces, are important for the modeling of radiationless decay mechanisms in photochemical processes. Here, we demonstrate that accurate non-adiabatic couplings can be calculated in the framework of linear-response time-dependent density functional theory by using non-empirical, optimally-tuned range-separated hybrid (OT-RSH) functionals. We focus on molecular radicals, in which ultrafast non-radiative decay plays a crucial role, to find that the OT-RSH functional compares well to wave-function based reference data and competes with the accuracy of semi-empirical CAM-B3LYP calculations. Our findings show that the OT-RSH approach provides very accurate non-adiabatic couplings and, therefore, provides a computationally efficient alternative to wave-function based techniques.

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

Ultrafast time-resolved polarization-dependent investigations on the dynamics in the Ã2B2 state of NO2 molecules

We perform time-resolved polarization-dependent study on ultrafast dynamics in the à 2 B 2  state of NO 2 . A linearly-polarized 400 nm femtosecond laser is used to resonantly pump NO 2 to its first excited state à 2 B 2 , and the time-dependent ionic yields produced via strong field ionization at 800 nm are measured under different laser polarizations. The yield ratios measured with the lasers perpendicular and parallel to each other first decrease then increase as the wave packet evolves on the excited state, with a minimum ratio at the delay time of 180 fs, which can be attributed to the evolution time in the à 2 B 2 state. The behavior of the time-resolved ionization in elliptically polarized laser field is also investigated and discussed. Our study indicates that the time-resolved polarization-dependent studies will shed some light on and pave the way to understand ultrafast dynamics in molecular excited states.

Non-Born-Oppenheimer effects in molecular photochemistry: an experimental perspective

Non-adiabatic couplings between Born-Oppenheimer (BO)-derived potential energy surfaces are now recognized as pivotal in describing the non-radiative decay of electronically excited molecules following photon absorption. This opinion piece illustrates how non-BO effects provide photostability to many biomolecules when exposed to ultraviolet radiation, yet in many other cases are key to facilitating 'reactive' outcomes like isomerization and bond fission. The examples are presented in order of decreasing molecular complexity, spanning studies of organic sunscreen molecules in solution, through two families of heteroatom containing aromatic molecules and culminating with studies of isolated gas phase H₂O molecules that afford some of the most detailed insights yet available into the cascade of non-adiabatic couplings that enable the evolution from photoexcited molecule to eventual products. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

Generalized Ab Initio Nonadiabatic Dynamics Simulation Methods from Molecular to Extended Systems

Nonadiabatic dynamics simulation has become a powerful tool to describe nonadiabatic effects involved in photophysical processes and photochemical reactions. In the past decade, our group has developed generalized trajectory-based ab initio surface-hopping (GTSH) dynamics simulation methods, which can be used to describe a series of nonadiabatic processes, such as internal conversion, intersystem crossing, excitation energy transfer and charge transfer of molecular systems, and photoinduced nonadiabatic carrier dynamics of extended systems with and without spin-orbit couplings. In this contribution, we will first give a brief introduction to our recently developed methods and related numerical implementations at different computational levels. Later, we will present some of our latest applications in realistic systems, which cover organic molecules, biological proteins, organometallic compounds, periodic organic and inorganic materials, etc. Final discussion is given to challenges and outlooks of ab initio nonadiabatic dynamics simulations.

Dynamic signatures of electronically nonadiabatic coupling in sodium hydride: a rigorous test for the symmetric quasi-classical model applied to realistic, ab initio electronic states in the adiabatic representation

Sodium hydride (NaH) in the gas phase presents a seemingly simple electronic structure making it a potentially tractable system for the detailed investigation of nonadiabatic molecular dynamics from both computational and experimental standpoints. The single vibrational degree of freedom, as well as the strong nonadiabatic coupling that arises from the excited electronic states taking on considerable ionic character, provides a realistic chemical system to test the accuracy of quasi-classical methods to model population dynamics where the results are directly comparable against quantum mechanical benchmarks. Using a simulated pump-probe type experiment, this work presents computational predictions of population transfer through the avoided crossings of NaH via symmetric quasi-classical Meyer-Miller (SQC/MM), Ehrenfest, and exact quantum dynamics on realistic, ab initio potential energy surfaces. The main driving force for population transfer arises from the ground vibrational level of the D¹Σ⁺ adiabatic state that is embedded in the manifold of near-dissociation C¹Σ⁺ vibrational states. When coupled through a sharply localized first-order derivative coupling most of the population transfers between t = 15 and t = 30 fs depending on the initially excited vibronic wavepacket. While quantum mechanical effects are expected due to the reduced mass of NaH, predictions of the population dynamics from both the SQC/MM and Ehrenfest models perform remarkably well against the quantum dynamics benchmark. Additionally, an analysis of the vibronic structure in the nonadiabatically coupled regime is presented using a variational eigensolver methodology.

A new permutation-symmetry-adapted machine learning diabatization procedure and its application in MgH2 system

This work introduces a new permutation-symmetry-adapted machine learning diabatization procedure, termed the diabatization by equivariant neural network (DENN). In this approach, the permutation symmetric and anti-symmetric elements in diabatic potential energy metrics (DPEMs) were simultaneously simulated by the equivariant neural network. The diabatization by deep neural network scheme was adopted for machine learning diabatization, and non-zero diabatic coupling was included to increase accuracy in the near degenerate region. Based on DENN, the global DPEMs for 1¹A' and 2¹A' states of MgH₂ have been constructed. To the best of our knowledge, these are the first global DPEMs for the MgH₂ system. The root-mean-square-errors (RMSEs) for diagonal elements (H₁₁ and H₂₂) and the off-diagonal element (H₁₂) around the conical intersection region were 5.824, 5.307, and 5.796 meV, respectively. The RMSEs of global adiabatic energies for two adiabatic states were 4.613 and 12.755 meV, respectively. The spectroscopic calculations of the 1¹A' state in the linear HMgH region are in good agreement with the experiment and previous theoretical results. The differences between calculated frequencies and corresponding experiment values are 1.38 and 1.08 cm^-1 for anti-symmetric stretching fundamental vibrational frequency and first overtone. The global DPEMs obtained in this work should be useful for further quantum mechanics dynamic simulations on the MgH₂ system.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

Conical intersection seams in spin-orbit coupled systems with an even number of electrons: A numerical study based on neural network fit surfaces

In this work, we consider the existence and topography of seams of conical intersections (CIs) for two key singlet-triplet systems, including a uniformly scaled spin-orbit interaction. The basic one triplet and one singlet state system denoted as (S₀,T₁) and the two singlets and one triplet system denoted as (S₀,S₁,T₁) are treated. Essential to this analysis are realistic electronic structure data taken from a recently reported neural network fit for the 1,2¹A and 1³A states of NH₃, including H_sf (spin-free) and H_so (spin-orbit) surfaces derived from high quality ab initio wavefunctions. Three types of seams for the (S₀,S₁,T₁) system are reported, which depend on the choice of the electronic Hamiltonian, H^e. The nonrelativistic CI seam [H^e = H_sf, (S₀,S₁)], the energy minimized nonrelativistic singlet-triplet intersection seam [H^e = H_sf, (S₀,T₁)], and the fully relativistic seam in the spin-diabatic representation (H^e = H_tot = H_sf + H_so) are reported as functions of R(N-H). The derivative couplings are computed using H^e = H_tot and H_sf from the fit data. The line integral of the derivative coupling is employed to juxtapose the geometric phase in the relativistic, H^e = H_tot, and nonrelativistic, H^e = H_sf, cases. It is found for the (S₀,T₁) system that there is no CI in the spin-adiabatic representation, while for the (S₀,S₁,T₁) system, CI can only be formed for two pairs of spin-adiabatic electronic states. The geometric phase effect thus needs to be handled with care when it comes to spin-nonconserving dynamics simulations.

Intersystem crossing and internal conversion dynamics with GAIMS-TeraChem: Excited state relaxation in 2-cyclopentenone

Excited states relaxation in complex molecules often involves two types of nonradiative transitions, internal conversion (IC) and intersystem crossing (ISC). In the situations when the timescales of IC and ISC are comparable, an interplay between these two types of transitions can lead to complex nonadiabatic dynamics on multiple electronic states of different characters and spin multiplicities. We demonstrate that the generalized ab initio multiple spawning (GAIMS) method interfaced with the fast graphics processing unit-based TeraChem electronic structure code can be used to model such nonadiabatic dynamics involving both the IC and ISC transitions in molecules of moderate size. We carried out 1500 fs GAIMS simulations leading to the creation of up to 2500 trajectory basis functions to study the excited states relaxation in 2-cyclopentenone. After a vertical excitation from the ground state to the bright S₂ state, the molecule quickly relaxes to the S₁ state via conical intersection. The following relaxation proceeds along two competing pathways: one involves IC to the ground state, and the other is dominated by ISC to the low-lying triplet states. The time constants describing the population transfer between the six lowest singlet and triplet states predicted by the GAIMS dynamics are in good agreement with the characteristic times of IC and ISC obtained from the analysis of the time-resolved photoelectron spectrum.

On the inclusion of one double within CIS and TDDFT

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

Stereodynamic Control of Collision-Induced Nonadiabatic Dynamics of NO (A2Σ+) with H2, N2, and CO: Intermolecular Interactions Drive Collision Outcomes

Intermolecular interactions, stereodynamics, and coupled potential energy surfaces (PESs) all play a significant role in determining the outcomes of molecular collisions. A detailed knowledge of such processes is often essential for a proper interpretation of spectroscopic observations. For example, nitric oxide (NO), an important radical in combustion and atmospheric chemistry, is commonly quantified using laser-induced fluorescence on the A²Σ⁺ ← X²Π transition band. However, the electronic quenching of NO (A²Σ⁺) with other molecular species provides alternative nonradiative pathways that compete with fluorescence. While the cross sections and rate constants of NO (A²Σ⁺) electronic quenching have been experimentally measured for a number of important molecular collision partners, the underlying photochemical mechanisms responsible for the electronic quenching are not well understood. In this paper, we describe the development of high-quality PESs that provide new physical insights into the intermolecular interactions and conical intersections that facilitate the branching between the electronic quenching and scattering of NO (A²Σ⁺) with H₂, N₂, and CO. The PESs are calculated at the EOM-EA-CCSD/d-aug-cc-pVTZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory, an approach that ensures a balanced treatment of the valence and Rydberg electronic states and an accurate description of the open-shell character of NO. Our PESs show that H₂ is incapable of electronically quenching NO (A²Σ⁺) at low collision energies; instead, the two molecules will likely undergo scattering. The PESs of NO (A²Σ⁺) with N₂ and CO are highly anisotropic and demonstrate evidence of electron transfer from NO (A²Σ⁺) into the lowest unoccupied molecular orbital of the collision partner, that is, the harpoon mechanism. In the case of ON + CO, the PES becomes strongly attractive at longer intermolecular distances and funnels population to a conical intersection between NO (A²Σ⁺) + CO and NO (X²Π) + CO. In contrast, for ON + N₂, the conical intersection is preceded by an ∼0.40 eV barrier. Overall, our work shines new light into the impact of coupled PESs on the nonadiabatic dynamics of open-shell systems.

Conformer-specific photochemistry imaged in real space and time

[Figure: see text].

Multiphoton Control of 6π Photocyclization via State-Dependent Reactant-Product Correlations

Multiphoton excitation promises opportunities for opening new photochemical reaction pathways and controlling photoproduct distributions. We demonstrate photonic control of the 6π photocyclization of ortho-terphenyl to make 4a,4b-dihydrotriphenylene (DHT). Using pump-repump-probe spectroscopy we show that 1 + 1' excitation to a high-lying reactant electronic state generates a metastable species characterized by a red absorption feature that accompanies a repump-induced depletion in the one-photon trans-dihydro product (trans-DHT); signatures of the new photoproduct are clearer for a structural analogue of the reactant that is sterically inhibited against one-photon cyclization. Quantum-chemical computations support assignment of this species to cis-DHT, which is accessible photochemically along a disrotatory coordinate from high-lying electronic states reached by 1 + 1' excitation. We use time-resolved spectroscopy to track photochemical dynamics producing cis-DHT. In total, we demonstrate that selective multiphoton excitation opens a new photoreaction channel in these photocyclizing reactants by taking advantage of state-dependent correlations between reactant and product electronic states.

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiff base C5H6NH2. J Chem Phys 2021;155:124111. [PMID: 34598550 DOI: 10.1063/5.0062757]

Nonadiabatic trajectory surface hopping simulations are reported for trans-C₅H₆NH₂ ⁺, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C₅H₆NH₂ ⁺, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S₁/S₀ conical intersections is immaterial to the photodynamics.

On the Importance of Ligand-Centered Excited States in the Emission of Cyclometalated Ir(III) Complexes

The photophysical behavior of the cyclometalating Ir(III) complexes [Ir(ppy)₂(bpy)]⁺, where Hppy is 2-phenylpyridine and bpy is 2,2′-bipyridine (complex 1), and [Ir(diFppy)₂(dtb-bpy)]⁺, where diFppy is 2-(2,4-difluorophenyl)pyridine and dtb-bpy is 4,4′-di-tert-butyl-2,2′-bipyridine (complex 2), has been theoretically investigated by performing density functional theory calculations. The two complexes share the same molecular skeleton, complex 2 being derived from complex 1 through the addition of fluoro and tert-butyl substituents, but present notable differences in their photophysical properties. The remarkable difference in their emission quantum yields (0.196 for complex 1 in dichloromethane and 0.71 for complex 2 in acetonitrile) has been evaluated by characterizing both radiative and nonradiative decay paths. It has emerged that the probability of decaying through the nonradiative triplet metal-centered state, normally associated with the loss of the emission quantum yield, does not appear to be the reason behind the reported substantially different emission efficiency. A more critical factor appears to be the ability of complex 2 to emit from both the usual metal-to-ligand charge-transfer state and from two additional ligand-centered states, as supported by the fact that the respective minima belong to the potential energy surface of the lowest triplet T₁ state and that their phosphorescence lifetimes are in the same order of magnitude. In contrast, the emission of complex 1 can be originated only from the metal-to-ligand charge-transfer state, being the only emissive T₁ minimum. The results constitute a significant case in which the emission from ligand-centered states is the key for determining the high emission quantum yield of a complex.

The reasons behind the significant increase in the emission quantum yield of the [Ir(diFppy)₂(dtb-bpy)]⁺ complex with respect to [Ir(ppy)₂(bpy)]⁺ are rationalized on the basis of DFT, TDDFT, and TDDFT-SOC calculations, revealing the key role that low-lying LC states can play in the emission properties of the complex.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Polariton induced conical intersection and berry phase

We investigate the Polariton induced conical intersection (PICI) created from coupling a diatomic molecule with the quantized photon mode inside an optical cavity, and the corresponding Berry Phase effects. We use the rigorous Pauli-Fierz Hamiltonian to describe the quantum light-matter interactions between a LiF molecule and the cavity, and use the exact quantum propagation to investigate the polariton quantum dynamics. The molecular rotations relative to the cavity polarization direction play a role as the tuning mode of the PICI, resulting in an effective CI even within a diatomic molecule. To clearly demonstrate the dynamical effects of the Berry phase, we construct two additional models that have the same Born-Oppenheimer surface, but the effects of the geometric phase are removed. We find that when the initial wavefunction is placed in the lower polaritonic surface, the Berry phase causes a π phase-shift in the wavefunction after the encirclement around the CI, indicated from the nuclear probability distribution. On the other hand, when the initial wavefunction is placed in the upper polaritonic surface, the geometric phase significantly influences the couplings between polaritonic states and therefore, the population dynamics between them. These BP effects are further demonstrated through the photo-fragment angular distribution. PICI created from the quantized radiation field has the promise to open up new possibilities to modulate photochemical reactivities.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Unlocking the Double Bond in Protonated Schiff Bases by Coherent Superposition of S1 and S2

The primary event occurring during the E-to-Z photoisomerization reaction of retinal protonated Schiff base (rPSB) is single-to-double bond inversion. In this work we examine the nuclear dynamics that occurs when the initial excited state is a superposition of the S₁ and S₂ electronic excited states that might be created in a laser experiment. The nuclear dynamics is dominated by double bond inversion that is parallel to the derivative coupling vector of S₁ and S₂. Thus, the molecule behaves as if it were at a conical intersection even if the states are nondegenerate.

Spiers Memorial Lecture: Introduction to ultrafast spectroscopy and imaging of photochemical reactions

A brief overview is presented on ultrafast spectroscopy and imaging of photochemical reactions by highlighting several experimental studies reported in the last five years. A particular focus is placed on new experiments performed using high-order harmonic generation, X-ray free electron lasers, and relativistic electron beams. Exploration of fundamental chemical reaction dynamics using these advanced experimental methodologies is in an early stage, and exciting new research opportunities await in this rapidly expanding and advancing research field. At the same time, there is no experimental methodology that provides all aspects of the electronic and structural dynamics in a single experiment, and investigations using different methodologies with various perspectives need to be considered in a comprehensive manner.

Exploring the effects of quantum decoherence on the excited-state dynamics of molecular systems

Fewest-switches surface hopping (FSSH) is employed in order to investigate the nonadiabatic excited-state dynamics of thiophene and related compounds and hence to establish a connection between the electronic system, the critical points in configuration space and the deactivation dynamics. The potential-energy surfaces of the studied molecules were calculated with complete active space self-consistent field and time-dependent density-functional theory. They are analyzed thoroughly to locate and optimize minimum-energy conical intersections, which are essential to the dynamics of the system. The influence of decoherence on the dynamics is examined by employing different decoherence schemes. We find that irrespective of the employed decoherence algorithm, the population dynamics of thiophene give results which are sound with the expectations grounded on the analysis of the potential-energy surface. A more detailed look at single trajectories as well as on the excited-state lifetimes, however, reveals a substantial dependence on how decoherence is accounted for. In order to connect these findings, we describe how ensemble averaging cures some of the overcoherence problems of uncorrected FSSH. Eventually, we identify carbon–sulfur bond cleavage as a common feature accompanying electronic transitions between different states in the simulations of all thiophene-related compounds studied in this work, which is of interest due to their relevance in organic photovoltaics.

Control of nuclear dynamics in the benzene cation by electronic wavepacket composition

The study of coupled electron-nuclear dynamics driven by coherent superpositions of electronic states is now possible in attosecond science experiments. The objective is to understand the electronic control of chemical reactivity. In this work we report coherent 8-state non-adiabatic electron-nuclear dynamics simulations of the benzene radical cation. The computations were inspired by the extreme ultraviolet (XUV) experimental results in which all 8 electronic states were prepared with significant population. Our objective was to study the nuclear dynamics using various bespoke coherent electronic state superpositions as initial conditions in the Quantum-Ehrenfest method. The original XUV measurements were supported by Multi-configuration time-dependent Hartree (MCTDH) simulations, which suggested a model of successive passage through conical intersections. The present computations support a complementary model where non-adiabatic events are seen far from a conical intersection and are controlled by electron dynamics involving non-adjacent adiabatic states. It proves to be possible to identify two superpositions that can be linked with two possible fragmentation paths.

Strong Field Ionization-Photofragmentation on Ultrafast Evolution of Electronic States of Toluene Cations

Ultrafast time-resolved strong field ionization-photofragmentation (SFI-PF) has emerged as a useful method for investigation of dynamics of molecular cations. Here we perform a SFI-PF study on the electronic states of toluene cations. By measuring the ion yields as a function of delay time, we obtain the transients of both parent and daughter ions, which show ultrafast decays and out-of-phase oscillations. The results provide the first experimental evidence of D₁-D₀ ultrafast relaxation of toluene cations occurring in about 530 fs and indicate coincident resonance between the vibrational states in D₁ and D₀ leading to oscillations with a period of about 2.05 ps. Our study should shed some light on the ultrafast photochemistry involving complex molecular cations.

CAS without SCF-Why to use CASCI and where to get the orbitals

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree-Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Finally, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

Waveform control of molecular dynamics close to a conical intersection

Conical intersections are ubiquitous in chemical systems but, nevertheless, extraordinary points on the molecular potential energy landscape. They provide ultra-fast radiationless relaxation channels, their topography influences the product branching, and they equalize the timescales of the electron and nuclear dynamics. These properties reveal optical control possibilities in the few femtosecond regime. In this theoretical study, we aim to explore control options that rely on the carrier envelope phase of a few-cycle IR pulse. The laser interaction creates an electronic superposition just before the wave packet reaches the conical intersection. The imprinted phase information is varied by the carrier envelope phase to influence the branching ratio after the conical intersection. We test and analyze this scenario in detail for a model system and show to what extent it is possible to transfer this type of control to a realistic system like uracil.