Exploring the Many-Body Dynamics Near a Conical Intersection with Trapped Rydberg Ions.

Combining the strong, long-range interactions of cold Rydberg atoms with the controllability of trapped ions, trapped Rydberg ions provide a promising platform for scalable quantum information processing. As demonstrated in a breakthrough experiment [1], microwave dressing of Rydberg states induces permanent rotating dipole moments leading to strong interactions between highly excited ions. Due to the separation of timescales, the fast electronic dynamics of Rydberg ions decouple from the slower motional modes of the linear Coulomb crystal, which typically mediate entangling gates in ground-state ion systems. Therefore, Rydberg ions enable significantly faster gate operations. We demonstrate how the unique properties of trapped Rydberg ions can be exploited to realize fast and high-fidelity entangling gates, along with the associated challenges and strategies to overcome them. Different types of gate protocols for two- and three-qubit entangling gates with trapped Rydberg ions are presented and sources of infidelity are analyzed.

Preface 1. Overview: Accurate Description of Low-Lying Electronic States and Potential Energy Surfaces 2. Simultaneous Account of Dynamic and Nondynamic Correlations Based on Complementarity of CI and CC Approaches 3. Method of Moments of Coupled-Cluster Equations: A New Theoretical Framework for Designing Black-Box Approaches for Molecular Potential Energy Surfaces 4. The Photoelectron Spectrum of the NO3 Radical Revisited: A Theoretical Investigation of Potential Energy Surfaces and Conical Intersections 5. Coupled Cluster Methods for Bond-Breaking 6. State-Specific Multireference Coupled Cluster-Based Methods for Potential Energy Surfaces and Their Approximate Variants 7. The Excited and Ion States of Allene 8. Hamiltonian Matrix Elements for the Table-CI Method Using Genealogical Configuration State Functions 9. Jacob's Ladder for Time-Dependent Density-Functional Theory: Some Rungs on the Way to Photochemical Heaven 10. Spectral Theory of Chemical Bonding 11. Comparison of CaF, ZnF, CaO, and ZnO: Their Anions and Cations in Their Ground and Low-Lying Excited States 12. The X1(2(3/2) and X2(2(1/2) Potentials of the Halogen Monoxides: A Comparison of RKR and Ab Initio Results 13. Symmetry in Spin-Orbit Coupling 14. Non-Adiabatic Bending Dissociation of OCS Induced by Orbital Unlocking 15. Electronic Structure and Dynamics in the O4 System 16. Model Studies of Intersystem Crossing Effects in the O + H2 Reaction 17. The Challenge of High-Resolution Dynamics: Rotationally Mediated Unimolecular Dissociation of HOCl 18. The Electronic Adiabatic-to-Diabatic Transformation Matrix and the Irreducible Representation of the Rotation Group 19. Spectroscopic Determination of Potential Energy Surfaces for the Out-of-Plane Ring Vibrations of Indan and Related Molecules in Their S0 and S1 ((, (*) States 20. Semiclassical Time Evolution in the Forward-Backward Stationary-Phase Limit 21. Development and Application of an Ab Initio Methane-Water Potential for the Study of Phase Equilibria of Methane Hydrates Indexes Author Index Subject Index

The structural dynamics of a molecule are determined by the underlying potential energy landscape. Conical intersections are funnels connecting otherwise separate potential energy surfaces. Posited almost a century ago1, conical intersections remain the subject of intense scientific interest2-5. In biology, they have a pivotal role in vision, photosynthesis and DNA stability6. Accurate theoretical methods for examining conical intersections are at present limited to small molecules. Experimental investigations are challenged by the required time resolution and sensitivity. Current structure-dynamical understanding of conical intersections is thus limited to simple molecules with around ten atoms, on timescales of about 100 fs or longer7. Spectroscopy can achieve better time resolutions8, but provides indirect structural information. Here we present few-femtosecond, atomic-resolution videos of photoactive yellow protein, a 2,000-atom protein, passing through a conical intersection. These videos, extracted from experimental data by machine learning, reveal the dynamical trajectories of de-excitation via a conical intersection, yield the key parameters of the conical intersection controlling the de-excitation process and elucidate the topography of the electronic potential energy surfaces involved.

In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These surfaces may intersect at a point in the nuclear coordinates with the topology of a double cone. These conical intersections have important consequences for the dynamics. When an adiabatic electronic wave function is transported around a closed loop in nuclear coordinate space that encloses a conical intersection point, it acquires an additional geometric, or Berry, phase. The Schr\"odinger equation for nuclear motion must be modified accordingly. A conical intersection also permits efficient nonadiabatic transitions between potential-energy surfaces. Most examples of the geometric phase in molecular dynamics have been in situations in which a molecular point-group symmetry required the electronic degeneracy and the consequent conical intersection. Similarly, it has been commonly assumed that the conical intersections facilitating nonadiabatic transitions were largely symmetry driven. However, conical intersections also occur in the absence of any symmetry considerations. This review discusses computational tools for finding and characterizing the conical intersections in such systems. Because these purely accidental intersections are difficult to anticipate, they may occur more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena. [S0034-6861(96)00404-7]

Optical control of dynamic processes has been challenging yet has only been demonstrated in several chemical and biological systems. The control of a reaction passing the widely present conical intersection has not been realized. Here, we modulated the phase of the excitation pulse to control the dynamics of β-carotene through accessing the conical intersection (CI). We observed different dynamics in 110-220 fs into the CI and the consecutive process in 400-600 fs through another CI by various chirped excitation pulses. We successfully controlled those ultrafast wavepacket dynamics passing the CIs on the femtosecond time scales. The method developed here can be used to control a various of ultrafast chemical and biological reactions through the CI(s).

Conical intersections represent critical topological features of potential energy surfaces and open ultrafast nonradiative deactivation channels for photoexcited molecules. In the following, we investigate how this funneling picture is transposed in the eyes of the exact factorization formalism for a 2D model system. The exact factorization of the total molecular wave function leads to the fundamental concept of time-dependent potential energy surface and time-dependent vector potential, whose behavior during a dynamics through a conical intersection has up to now remained unexplored. Despite the fact that these quantities might be viewed as time-dependent generalizations of the adiabatic potential energy surfaces and the nonadiabatic coupling vectors, characteristic quantities appearing in the Born-Oppenheimer framework, we observe that they do not exhibit particular topological features in the region of conical intersection but still reflect the complex dynamics of the nuclear wavepacket.

In this paper we present two new algorithms to study the extended nature of the crossing seam between electronic potential energy surfaces. The first algorithm is designed to optimize conical intersection geometries: both minima and saddle points. In addition, this method will optimize conical intersection geometries using arbitrary geometrical constraints. We demonstrate its potential on different crossing seams of benzene, z-penta-3,5-dieniminium, and 1,3-butadiene. The second algorithm is designed to explicitly compute the intersection-space minimum energy coordinate. Our computations show how an intersection seam and the energy along it can be unambiguously defined. A finite region of the S0/S1 1,3-butadiene crossing seam has been mapped out, and a new saddle point linked with two lower-lying geometries on the seam.

Location of conical intersections by the Pancharatnam connection and the sign-change theorem of Longuet-Higgins: a model calculation with the H4 potential surface

The fragmentation dynamics of gas phase phenol molecules following excitation at many wavelengths in the range 279.145 > or = lambdaphot > or = 206.00 nm have been investigated by H Rydberg atom photofragment translational spectroscopy. Many of the total kinetic energy release (TKER) spectra so derived show structure, the analysis of which confirms the importance of O-H bond fission and reveals that the resulting phenoxyl cofragments are formed in a very limited subset of their available vibrational state density. Spectra recorded at lambdaphot > or = 248 nm show a feature centered at TKER approximately 6500 cm(-1). These H atom fragments, which show no recoil anisotropy, are rationalized in terms of initial S1<--S0 (pi*<--pi) excitation, and subsequent dissociation via two successive radiationless transitions: internal conversion to ground (S0) state levels carrying sufficient O-H stretch vibrational energy to allow efficient transfer towards, and passage around, the conical intersection (CI) between the S0 and S2(1pisigma*) potential energy surfaces (PESs) at larger R(O-H), en route to ground state phenoxyl products. The observed phenoxyl product vibrations indicate that parent modes nu16a and nu11 can both promote nonadiabatic coupling in the vicinity of the S0S2 CI. Spectra recorded at lambdaphot < or = 248 nm reveal a faster, anisotropic distribution of recoiling H atoms, centered at TKER approximately 12,000 cm(-1). These we attribute to H+phenoxyl products formed by direct coupling between the optically excited S1(1pi pi*) and repulsive S2(1pi sigma*) PESs. Parent mode nu16b is identified as the dominant coupling mode at the S1/S2 CI, and the resulting phenoxyl radical cofragments display a long progression in nu18b, the C-O in-plane wagging mode. Analysis of all structured TKER spectra yields D0(H-OC6H5) = 30,015 +/- 40 cm(-1). The present findings serve to emphasize two points of wider relevance in contemporary organic photochemistry: (i) The importance of 1) pi sigma* states in the fragmentation of gas phase heteroaromatic hydride molecules, even in cases where the 1pi sigma* state is optically dark. (ii) The probability of observing strikingly mode-specific product formation, even in "indirect" predissociations, if the fragmentation is driven by ultrafast nonadiabatic couplings via CIs between excited (and ground) state PESs.

The dissociation dynamics of trans-azomethane upon excitation to the S,(n, pi) state with a total energy of 93 kcalmol-1 is investigated using femtosecond-resolved mass spectrometry in a molecular beam. The transient signal shows an opposite pump-probe excitation feature for the UV (307 nm) and the visible (615 nm) pulses at the perpendicular polarization in comparison with the signal obtained at the parallel polarization: The one-photon symmetry-forbidden process excited by the UV pulse is dominant at the perpendicular polarization, whereas the two-photon symmetry-allowed process initiated by the visible pulse prevails at the parallel polarization. At the perpendicular polarization, we found that the two C-N bonds of the molecule break in a stepwise manner, that is, the first C-N bond breaks in approximately 70 fs followed by the second one in approximately 100 fs, with the intermediate characterized. At the parallel polarization, the first C-N bond cleavage was found to occur in 100 fs with the intensity of the symmetry-allowed transition being one order of magnitude greater than the intensity of the symmetry-forbidden transition at the perpendicular polarization. Theoretical calculations using time-dependent density functional theory (TDDFT) and the complete active space self-consistent field (CASSCF) method have been carried out to characterize the potential energy surface for the ground state, the low-lying excited states, and the cationic ground state at various levels of theory. Combining the experimental and theoretical results, we identified the elementary steps in the mechanism. The initial driving force of the ultrafast bond-breaking process of trans-azomethane (at the perpendicular polarization) is due to the CNNC torsional motion initiated by the vibronic coupling through an intensity-borrowing mechanism for the symmetry-forbidden n-pi transition. Following this torsional motion and the associated molecular symmetry breaking, an S0/S1 conical intersection (CI) can be reached at a torsional angle of 93.1 degrees (predicted at the CASSCF(8.7)/cc-pVDZ level of theory). Funneling through the S0/S1, CI could activate the asymmetric C-N stretching motion, which is the key motion for the consecutive C-N bond breakages on the femtosecond time scale.

We report on the spectra and dynamics of H3 near the conical intersection in its (2p)1E′ ground electronic manifold. The time-dependent wave packet approach and the double many-body expansion (DMBE) potential energy surface (PES) are employed for this purpose. We use Jacobi coordinates (R,r,γ) and employ the fast Fourier transform method for R and r, and the discrete variable representation method for γ, in conjunction with the split-operator formalism to describe the evolution of the wave packet (WP) in space and time, respectively. While the main focus of the present work is to explicitly reveal the effects of nonadiabatic coupling between the two sheets of the DMBE PES, companion calculations are also carried out to investigate the dynamics on the uncoupled upper and lower adiabatic sheets, both in two and three dimensions (for total angular momentum J=0). A set of pseudospectra is calculated by Fourier transforming the time autocorrelation function of suitably chosen Gaussian wave packets located initially at the minimum energy point of the seam of conical intersections. The eigenstates thus obtained are assigned by computing their eigenfunctions by spectral quantization. In the coupled states treatment the WP is propagated in the diabatic representation. The time dependence of the adiabatic populations is calculated by using suitable adiabatic projection operators. We find strong effects of nonadiabatic coupling on the discrete vibrational energy levels of the upper adiabatic sheet, which all change to quasibound states in the coupled manifold. The comparison of the decay dynamics of various levels of the upper adiabatic sheet indicates considerable mode specificity (their lifetimes typically vary between 3 and 6 fs). On the other hand, resonances are seen to be less pronounced near the conical intersection on the lower adiabatic sheet (when compared to those in the literature, obtained near the collinear saddle point region). The effect of nonadiabatic coupling on them is only minor. We also report preliminary results on the optical emission spectrum of H3 and compare them with the experimental findings.

The photoisomerization of cis- and trans-stilbene through conical intersections (CI) is mainly governed by four dihedral angles around central C═C double bonds. The two of them are C-C═C-C and H-C═C-H dihedral angles that are found to form a mirror rotation coordinate, and the mirror plane appears at the two dihedral angles equal to zeros with which the middle state is defined through partial optimization. There exist the first-type of hula-twist-CI enantiomers, the second-type of hula-twist-CI enantiomers, the first-type of one-bond-flip-CI enantiomers, and the second type of one-bond-flip-CI enantiomers as well as cis-enantiomers and trans-enantiomers with respect to this mirror plane. The complete active space self-consistent field method is employed to calculate minimum potential energy profile along the mirror rotation coordinate for each enantiomers, and it is found that the left-hand manifold and the right-hand manifold of potential energy surfaces can be energetically transferred via photoisomerization. Furthermore, two-dimensional potential energy surfaces in terms of the branching plane g-h coordinates are constructed at vicinity of each conical intersection, and the landscapes of conical intersections show distinct feature, and in excited-state four potential wells separated in different section of g-h plane related to different conical intersections which indicate different photoisomerization pathways.

Conical intersections are perhaps the most significant mechanistic features of chemical reactions occurring through excited states. By providing funnels for efficient non-adiabatic population transfer, conical intersections govern the branching ratio of products of such reactions, similar to what the transition states do for ground-state reactivity. In this regard, intersections between the ground and the lowest excited states play a special role, and the correct description of the potential energy surfaces in their vicinity is crucial for understanding the mechanism and dynamics of excited-state reactions. The methods of density functional theory, such as time-dependent density functional theory, are widely used to describe the excited states of large molecules. However, are these methods suitable for describing the conical intersections or do they lead to artifacts and, consequently, to erroneous description of reaction dynamics? Here we address the first part of this question and analyze the ability of several density functional approaches, including the linear-response time-dependent approach as well as the spin-flip and ensemble formalisms, to provide the correct description of conical intersections and the potential energy surfaces in their vicinity. It is demonstrated that the commonly used linear-response time-dependent theory does not yield a proper description of these features and that one should instead use alternative computational approaches.

Quantum Chemical Study of Coupled Molecular Photoswitches

Electrophilic aromatic substitutions (EAS), one of the most extensively studied organic reactions, can be considered under certain circumstances as a photochemical reaction without light. Thermochemical considerations show that in the gas phase, the reaction system (electrophile plus aromatic neutral) is often found initially in an electronically excited state, whereas the reaction products are formed on the ground state potential energy surface (PES). The crossing to the ground state is usually very rapid, so that the rate-determining steps take place on the ground state surface. It is shown that after the crossing (through a conical intersection (CI)), the system can be found on different parts of the ground state potential surface. In particular, the CI is connected without a barrier to all moieties assumed to be important in the reaction (pi complex, radical pair, and sigma complex). In some cases, due to a relatively low electron affinity of the electrophile and bond reorganization, the reaction starts on the ground state PES; a conical intersection exists in these cases, but is not accessed by the reactants. The topology of the reaction surface due to the avoided crossing is reminiscent of that in which an actual crossing takes place. The paper provides a comprehensive model for several EAS reactions. The CIs are located computationally, and an energy level diagram is proposed for some representative EAS reactions.