Time-dependent Quantum Dynamics Research Articles

Adaptive Trotterization for Time-Dependent Hamiltonian Quantum Dynamics Using Piecewise Conservation Laws.

Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [H. Zhao et al., Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond, PRX Quantum 4, 030319 (2023).2691-339910.1103/PRXQuantum.4.030319]. We validate the algorithm for a time dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.

Dense outputs from quantum simulations

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time T and error tolerance ϵ. Our results demonstrate that the linearization approach can nearly achieve optimal complexity O(T/ϵ) for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning.

Theoretical study of S + SH reaction on its ground state HS2(X2 A ″) potential energy surface

ABSTRACT In this study, we explore the initial state selected dynamics of the S + SH ( X 2 Π ) → S 2 ( X 3 ∑ ) + H reaction through the lens of time-dependent quantum dynamics (QD), quasi-classical trajectory (QCT), and statistical quantum mechanical (SQM) approaches, utilising the electronic ground state HS 2 (X 2 A ′′ ) potential energy surface (PES). We present total reaction probabilities and integral cross sections (ICSs) as part of our findings. Our results indicate that at low and moderate collision energies, the reaction predominantly follows an indirect pathway, forming meta-stable quasi-bound complexes. Additionally, we observe that the rotational excitation of the SH reagent initially leads to a decrease and then an increase in reactivity. We conduct a comprehensive analysis and comparison of the outcomes from QD, QCT, and SQM methodologies.

The interplay of vibronic and spin-orbit coupling in the fluorescence quenching in trans-dithionated PDI.

Organic chromophores such as the thionated derivatives of perylene diimides (PDIs) show prolonged triplet-excited state lifetimes in contrast to their pristine parent PDI molecule, which shows near unity fluorescence quantum yield. The excited state dynamics in the trans-dithionated PDI (S2-PDI) are studied here. Unlike PDI, the photo absorbing ππ* state of S2-PDI is in close proximity to quasi-degenerate nπ* states. The latter exhibits an interesting vibronic problem leading to the breaking of orbital symmetry mediated through non-totally symmetric vibrations. The time-dependent quantum dynamics are studied with a diabatic model Hamiltonian involving three singlet and three triplet states coupled via 22 vibrational modes. A combined effect of multiple internal-conversion and inter-system crossing (ISC) pathways leads to population transfer from the 1ππ* state to the 3ππ* state via the nπ* states, with an overall ISC rate of 0.70ps that compares well with the experimental value. The calculated absorption spectra for PDI and S2-PDI reproduce the essential vibronic features in the observed experimental spectra. The dominant vibronic progressions are found to have significant contributions from the vinyl stretching modes of the PDI core.

Beyond Conventional Density Functional Theory: Advanced Quantum Dynamical Methods for Understanding Degradation of Per- and Polyfluoroalkyl Substances.

Computational chemistry methods, such as density functional theory (DFT), have now become more common in environmental research, particularly for simulating the degradation of per- and polyfluoroalkyl substances (PFAS). However, the vast majority of PFAS computational studies have focused on conventional DFT approaches that only probe static, time-independent properties of PFAS near stationary points on the potential energy surface. To demonstrate the rich mechanistic information that can be obtained from time-dependent quantum dynamics calculations, we highlight recent studies using these advanced techniques for probing PFAS systems. We briefly discuss recent applications ranging from ab initio molecular dynamics to DFT-based metadynamics and real-time time-dependent DFT for probing PFAS degradation in various reactive environments. These quantum dynamical approaches provide critical mechanistic information that cannot be gleaned from conventional DFT calculations. We conclude with a perspective of promising research directions and recommend that these advanced quantum dynamics simulations be more widely used by the environmental research community to directly probe PFAS degradation dynamics and other environmental processes.

Nonadiabatic Vibrational Resonance Raman Spectra from Quantum Dynamics Propagations with LVC Models. Application to Thymine.

We present a viable protocol to compute vibrational resonance Raman (vRR) spectra for systems with several close-lying and potentially coupled electronic states. It is based on the parametrization of linear vibronic coupling (LVC) models from time-dependent density functional theory (TD-DFT) calculations and quantum dynamics propagations of vibronic wavepackets with the multilayer version of the multiconfiguration time-dependent Hartree (ML-MCTDH) method. Our approach is applied to thymine considering seven coupled electronic states, comprising the three lowest bright states, and all vibrational coordinates. Computed vRR at different excitation wavelengths are in good agreement with the available experimental data. Up to 250 nm the signal is dominated by the lowest HOMO → LUMO transition, whereas at 233 nm, in the valley between the two lowest energy absorption bands, the contributions of all the three bright states, and their interferences and couplings, are important. Inclusion of solvent (water) effects improves the agreement with experiment, reproducing the coalescence of vibrational bands due to CC and C=O stretchings. With our approach we disentangle and assess the effect of interferences between the contribution of different quasi-resonant states to the transition polarizability and the effect of interstate couplings. Our findings strongly suggest that in cases of close-lying and potentially coupled states a simple inclusion of interference effects is not sufficient, and a fully nonadiabatic computation should instead be performed. We also document that for systems with strong couplings and quasi-degenerate states, the use of HT perturbative approach, not designed for these cases, may lead to large artifacts.

Time-Dependent Quantum Dynamics Study of the Interaction between Helium Atom and Synchrotron Radiation

For the first time, excitation and ionization of helium atom (He) induced by synchrotron radiation(SR) is simulated in the present work. It is found that electrons can tunnel through the ground state of helium atom and leave from the atomic region caused by subsequent SR field. Therefore, the ionization of He atom can happen. Additionally, some electrons can be captured by a higher electronic state, which leads to the tunneling excitation from the ground state to a specific excited state.

Quantum dynamics study of OH−+CH3I reaction: Reaction probability, integral cross section, and energy efficacy

We investigate the reaction probability, integral cross section, and energy efficiency of the OH−+CH3I reaction using the time-dependent quantum dynamics wave packet method. A four-degree-of-freedom dynamics model is developed for this study due to the synchronized SN2 bond-breaking and formation mechanism. We find that the reaction probability decreases as a function of the collision energy, which is a typical character of reactions with a negative energy barrier. The ground-state integral cross section calculated using this model is in excellent agreement with the quasi-classical trajectory results. The integral cross-section ratios of the vibrational excitations over the ground state, at the same equal amount of total energy, indicate that the vibrational motion of the CH3–I is more efficient in enhancing the reactivity than the translational motion, which, in turn, has a bigger contribution to the reactivity than the C–H3 vibrational motion. The energy efficacy order in the reactivity is confirmed by the sudden vector model prediction.

Time-dependent dynamics of nuclear spin symmetry and parity violation in dichlorodisulfane (ClSSCl) during and after coherent radiative excitation

Parity and nuclear spin symmetry are approximate symmetries, which for many primary processes in molecular spectroscopy and kinetics lead to almost exact constants of the motion. The symmetric isotopomer dichlorodisulfane (disulfur dichloride) is chiral with two enantiomers, each of which has also two nuclear spin isomers (ortho and para isomers). Electroweak quantum chemistry predicts a small ‘parity violating’ energy difference between the ground states of the enantiomers (M being more stable than P by about ). Furthermore recent microwave spectroscopy has indicated ‘forbidden’ transitions between ortho and para isomers. These phenomena allow for a comparative study of the time-dependent quantum dynamics of parity and nuclear spin symmetry violation in a chiral molecule for the first time. We report quantum dynamical calculations of coherent radiative excitation of the complex manifold of polyads with hyperfine structure in ClSSCl. We demonstrate almost complete (near 100%) transfer of population from an almost pure para-ground state to an almost pure excited ortho state. Short-pulse excitation from the para-ground state to an excited time-dependent para chromophore state shows intramolecular interconversion between para and ortho nuclear spin isomers under isolation after the pulse on a time scale of a few nanoseconds to a few microsecond depending on the excited polyad. We also demonstrate the preparation of exotic ‘chameleon states’, which are superpositions of energy eigenstates corresponding to ortho- and para- nuclear spin symmetry isomers at the same time. The results are discussed in relation to the strong separation of time scales between the primary processes of nuclear spin symmetry isomerisation (nanoseconds to microseconds) and parity change (seconds) and in relation to possible experiments to measure in this molecule. We also compare with the rate processes of nuclear spin symmetry isomerisation induced by thermal black body radiation, depending on temperature, occurring on time scales from less than seconds to more than 100 years.

Intersystem Crossing in Boron-Based Donor-Spiro-Acceptor Organic Chromophore: A Detailed Theoretical Study.

Intersystem crossing and reverse intersystem crossing (rISC) processes were investigated in a boron-based donor-spiro-acceptor organic chromophore which shows thermally activated delayed fluorescence. Due to the perpendicular arrangement between donor and acceptor moieties, the HOMO and the LUMO are spatially separated, and the compound shows charge transfer (CT) transitions. We found both S1 and T1 excited states are CT in nature (i.e., electron and hole wave functions are localized on acceptor and donor units, respectively) and T2, which is higher in energy than S1 and T1, is locally excited in nature (i.e., both electron and hole wave functions are localized on an acceptor unit). Because of the same nature of excitation (i.e., CT here), the spin-orbit coupling matrix element between S1 and T1 is very low and insignificant exciton conversion occurs from the T1 state to the S1 state (and vice versa). Our combined time-dependent density functional theory and quantum dynamics simulation shows that the rISC process from the T1 state to the S1 state can be enhanced by the presence of a nearby local excited triplet state (i.e., T2 state here). A smaller gap between the T1 and T2 states efficiently establishes the rISC route.

State-to-state dynamics of reactions H + DH’(ν = 0,j = 0) → HH’(ν’,j’) + D/HD(ν’,j’) + H’ with time-dependent quantum wave packet method* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11504206 and 12004216), the Ph. D. Research Start-up Fund of Shandong Jiaotong University (Grant No. BS2020025), and the Shandong Natural Science Foundation, China (Grant Nos.

State-to-state time-dependent quantum dynamics calculations have been carried out to study H + DH’ → HH’ + D/HD + H’ reactions on BKMP2 surface. The total integral cross sections of both reactions are in good agreement with earlier theoretical and experimental results, moreover the rotational state-resolved reaction cross sections of H + DH’ → HH’ + D at collision energy E C = 0.5 eV are closer to the experimental values than the ones calculated by Chao et al. [J. Chem. Phys. 117 8341 (2002)], which proves the higher precision of the quantum calculation in this work. In addition, the state-to-state dynamics of H + DH’ → HD’ + H reaction channel have been discussed in detail, and the differences of the micro-mechanism of the two reaction channels have been revealed and analyzed clearly.

Bayesian optimization for inverse problems in time-dependent quantum dynamics.

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schrödinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schrödinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with the Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduces the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO2 and propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.

Quantum dynamics studies of isotope effects in the Mg+(3p) + HD \u2192 MgH+/MgD+ + D/H insertion reaction

The time-dependent wave packet quantum dynamics studies for the Mg+(3p) + HD → MgH+/MgD+ + D/H diabatic reaction are carried out for the first time on recently developed diabatic YHWCH potential energy surfaces [Phys. Chem. Chem. Phys., 2018, 20, 6638–6647]. The results of reaction probabilities and total integral cross sections show a dramatic preference to the formation of MgD+ over MgH+ owing to the insertion reaction mechanism in the title reaction. The MgD+/MgH+ branching ratio witnesses a monotonic decrease from 10.58 to 3.88 at collision energy range of 0.01 to 0.20 eV, and at the collision energy of 0.114 eV, it is close to the experimental value of 5. The rovibrational state-resolved ICSs of the two channels show the products MgD+ have higher vibrational excitation and hotter rotational state distributions. The opacity function P(J) suggests that the MgH+ + D channel and MgD+ + H channel are dominated by high-b and low-b collisions, respectively. Both forward and backward scattering peaks are found in the differential cross section curves, whereas the angle distributions of products are not strictly forward-backward symmetric because of the short lifetime of the complex in the reaction.

How does the porphyrin-like vacancy affect the spectral properties of graphene quantum dots? A theoretical study

By processing graphene quantum dot, an ideal semiconductor material with suitable band gap and higher electron mobility can be obtained. Thus, it has a broad prospect in the application of photoelectric response materials. Here, a graphene defect with porphyrin-like structure is selected to achieve the controlable light absorption. The double five-membered-ring parallel vacancy are based on self-healing properties of popular graphene defects. Aimed to separate exciton and hole more effectively and achieve higher photoelectric conversion efficiency, the occupied orbital and unoccupied orbital of the quantum dot with objected defect structure is taken as orderly dispersion to form an obvious charge separation state under the demonstration with first principles calculation. Most importantly, a real time real space charge separation is calculated by time-dependent ab-initio quantum dynamics based on numerical atomic basis sets. The result shows the specific graphene defects can form an efficient pure graphene photoelectric response medium like porphyrin skeleton, and the vacancy will induce to adjust and control the specific wavelength of the response light and charge separated state manipulably with odevity of number of peripheral carbon rings by the calculation of ultrafast process.

Quantum dynamics study of isotope effects of the OD/OH + CH3 reactions

ABSTRACT A six-degrees-of-freedom, time-dependent quantum dynamics calculation is employed to study the integral cross sections, full-dimensional cumulative reaction probabilities and full-dimensional rate constants for the isotopic reactions of the OD and OH with CH3 reactions. The full-dimensional cumulative reaction probabilities and full-dimensional rate constants are obtained using the energy and J-K shifting approaches based on the six-degrees-of-freedom calculations. The comparison of integral cross sections shows that the OD + CH3 reaction has a larger energy threshold and a smaller tunnelling effect than the OH + CH3 reaction. The corrected rate constants using the experimental zero-point energy have a very good agreement with the experimental results. The comparison of the rate constants shows that the OD + CH3 has smaller rate constants than the OH + CH3 reaction, which indicates a smaller reactivity due to the isotope substitution.

Time-dependent density matrix renormalization group quantum dynamics for realistic chemical systems.

Electronic and/or vibronic coherence has been found by recent ultrafast spectroscopy experiments in many chemical, biological, and material systems. This indicates that there are strong and complicated interactions between electronic states and vibration modes in realistic chemical systems. Therefore, simulations of quantum dynamics with a large number of electronic and vibrational degrees of freedom are highly desirable. Due to the efficient compression and localized representation of quantum states in the matrix-product state (MPS) formulation, time-evolution methods based on the MPS framework, which we summarily refer to as tDMRG (time-dependent density-matrix renormalization group) methods, are considered to be promising candidates to study the quantum dynamics of realistic chemical systems. In this work, we benchmark the performances of four different tDMRG methods, including global Taylor, global Krylov, and local one-site and two-site time-dependent variational principles (1TDVP and 2TDVP), with a comparison to multiconfiguration time-dependent Hartree and experimental results. Two typical chemical systems of internal conversion and singlet fission are investigated: one containing strong and high-order local and nonlocal electron-vibration couplings and the other exhibiting a continuous phonon bath. The comparison shows that the tDMRG methods (particularly, the 2TDVP method) can describe the full quantum dynamics in large chemical systems accurately and efficiently. Several key parameters in the tDMRG calculation including the truncation error threshold, time interval, and ordering of local sites were also investigated to strike the balance between efficiency and accuracy of results.

Born oppenheimer and renner teller quantum dynamics of the ND + D reaction

The Born Oppenheimer (BO) and Renner Teller (RT) time dependent quantum dynamics are investigated for the reaction NDa1Δ+D′(2S), considering the NH2 electronic states X∼2B1 and A∼2A1. The introduction of RT effects opens the possibility of studying not only the adiabatic reactions (depletion- A N(2D) + D2(a1Δ) and Exchange ND’+(a1Δ) + D) but also non-adiabatic ones (quenching + exchange ND′(X3Σ-)+D, depletion- X N(4S) + D2(a1Δ)). The initial state resolved reaction probabilities, cross sections, and rate constants are obtained considering the Coriolis Coupling (CC) interactions for all the reactions above. To point out the role of RT and CC effect, we compared our results with experimental and semi- classical data.

Six-dimensional potential energy surfaces of the dissociative chemisorption of HCl on Ag(111) with three density functionals.

We first constructed six-dimensional potential energy surfaces (PESs) for the dissociative chemisorption of HCl on rigid Ag(111). Three global PESs were calculated using the neural network method based on extensive density functional theory (DFT) calculations with Perdew-Burke-Ernzerhof, Perdew-Wang91, and revised Perdew-Burke-Ernzerhof functionals, respectively. The resulting three PESs are all accurately fitted and smooth, based on the small fitting errors and good agreements between the fitted PESs and the direct DFT calculations. Time-dependent wave packet calculations show that the PESs are very well converged with respect to the fitting process, as well as the number of DFT data points. Comparisons of three PESs and time-dependent quantum dynamics results on the three PESs were given and discussed. The validity of site-averaging approximation holds for the title reaction, where the 25 site-averaged four-dimensional dissociation probability can accurately reproduce the six-dimensional dissociation probability on the current three PESs. We expect that the current theoretical investigations can stimulate the experimental work for this gas-surface reaction.

Quantum dynamics calculations reveal temperature independence of kinetic isotope effect of the OH + HBr/DBr reaction.

The reaction of OH radicals with HBr plays a key role in atmospheric chemistry as the reaction, OH + HBr → Br + H2O, produces Br atoms that destroy ozone. The experimental measurements of the kinetic isotope effect of k(OH + HBr)/k(OH + DBr) found that the kinetic isotope effects are temperature-independent. However, previous quasi-classical trajectory calculations on an accurate ab initio potential energy surface showed that the kinetic isotope effect is temperature-dependent. By contrast, the present full-dimensional time-dependent quantum dynamics calculations on the same potential energy surface find that the kinetic isotope effect is temperature-independent, agreeing well with the experimental studies both qualitatively and quantitatively. Furthermore, the rate constants from both quantum dynamics and quasi-classical trajectory calculations have a peak at around 15 K whereas the experimental data are not available in this low temperature range. The good agreement of the temperature-dependence of kinetic isotope effects between the present quantum dynamics calculations and the experimental measurements indicates that the kinetic isotope effect of k(OH + HBr)/k(OH + DBr) should be temperature-independent and the peak of the rate constants from the theoretical calculations call for experimental measurements at a very low temperature range.

Modeling Plasmon-Induced Hot-Carrier Transfer

In this issue of Chem , Zhang et al. use first-principle simulations (i.e., no empirically adjustable parameters) to elucidate the detailed mechanisms of plasmon-induced hot-carrier transfer at a heterojunction interface between a plasmonic gold nanomaterial and a semiconductor. Together with earlier work by Long and Prezhdo, this study shows how the donor-acceptor interaction at the interface determines the mechanism by which plasmonic excitations lead to hot-electron transfer at interfaces.